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Journal articles on the topic 'LAGRANGE MULTIPLIER TECHNIQUE'

Author: Grafiati

Published: 11 September 2023

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1

Galanin, M. P., V. V. Lukin, and P. V. Solomentseva. "Comparison of the Lagrange Multipliers Function Approximation Methods in Solving Contact Problems by the Independent Contact Boundary Technique." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 6 (105) (December 2022): 17–32. http://dx.doi.org/10.18698/1812-3368-2022-6-17-32.

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The paper considers the contact problem of the elasticity theory in a static spatial two-dimensional formulation without considering friction. For discretization of the elasticity theory equations, the finite element method was introduced using a triangular unstructured grid and linear and quadratic basis functions. To account for the contact boundary conditions, a modified method of Lagrange multipliers with independent contact boundary is proposed. This method implies the ability to construct a contact boundary with the smoothness degree required for the solution precision and to execute approximation of the Lagrange multiplier function independent of the grids inside the contacting bodies. Various types of the Lagrange multiplier function approximations were studied, including piecewise constant, continuous piecewise linear functions and piecewise linear functions with discontinuities at the difference cells boundaries. Examples of test calculations are provided both for problems with rectilinear and curvilinear contact boundaries. In both cases, the use of discontinuous approximations of the Lagrange multiplier function makes it possible to obtain a numerical solution with fewer artificial oscillations and higher rate of convergence at the grid refinement. It is shown that the numerical solution precision could be improved by more detailed discretization of the contact boundary without changing the grids inside the contacting bodies

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Matei, Andaluzia Cristina. "A Three-Field Variational Formulation for a Frictional Contact Problem with Prescribed Normal Stress." Fractal and Fractional 6, no. 11 (November 4, 2022): 651. http://dx.doi.org/10.3390/fractalfract6110651.

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In the present work, we address a nonlinear boundary value problem that models frictional contact with prescribed normal stress between a deformable body and a foundation. The body is nonlinearly elastic, the constitutive law being a subdifferential inclusion. We deliver a three-field variational formulation by means of a new variational approach governed by the theory of bipotentials combined with a Lagrange-multipliers technique. In this new approach, the unknown of the mechanical model is a triple consisting of the displacement field, a Lagrange multiplier related to the friction force and the Cauchy stress tensor. We obtain existence, uniqueness, boundedness and convergence results.

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3

Hu, Yun, and Qianqian Duan. "Solving the TSP by the AALHNN algorithm." Mathematical Biosciences and Engineering 19, no. 4 (2022): 3427–48. http://dx.doi.org/10.3934/mbe.2022158.

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<abstract> <p>It is prone to get stuck in a local minimum when solving the Traveling Salesman Problem (TSP) by the traditional Hopfield neural network (HNN) and hard to converge to an efficient solution, resulting from the defect of the penalty method used by the HNN. In order to mend this defect, an accelerated augmented Lagrangian Hopfield neural network (AALHNN) algorithm was proposed in this paper. This algorithm gets out of the dilemma of penalty method by Lagrangian multiplier method, ensuring that the solution to the TSP is undoubtedly efficient. The second order factor added in the algorithm stabilizes the neural network dynamic model of the problem, thus improving the efficiency of solution. In this paper, when solving the TSP by AALHNN, some changes were made to the TSP models of Hopfield and Tank. Say, constraints of TSP are multiplied by Lagrange multipliers and augmented Lagrange multipliers respectively, The augmented Lagrange function composed of path length function can ensure robust convergence and escape from the local minimum trap. The Lagrange multipliers are updated by using nesterov acceleration technique. In addition, it was theoretically proved that the extremum obtained by this improved algorithm is the optimal solution of the initial problem and the approximate optimal solution of the TSP was successfully obtained several times in the simulation experiment. Compared with the traditional HNN, this method can ensure that it is effective for TSP solution and the solution to the TSP obtained is better.</p> </abstract>

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Vyasarayani, C. P., Sukhpreet Singh Sandhu, and John McPhee. "Nonsmooth Modeling of Vibro-Impacting Euler-Bernoulli Beam." Advances in Acoustics and Vibration 2012 (September 12, 2012): 1–9. http://dx.doi.org/10.1155/2012/268595.

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A new technique to simulate nonsmooth motions occurring in vibro-impacting continuous systems is proposed. Sticking motions that are encountered during vibro-impact simulation are imposed exactly using a Lagrange multiplier, which represents the normal reaction force between the continuous system and the obstacle. The expression for the Lagrange multiplier is developed in closed form. The developed theory is demonstrated by numerically simulating the forced response of a pinned-pinned beam impacting a point-like rigid obstacle.

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Rodrigo, E., S. Tapia, J. M. Mera, and M. Soler. "Optimizing Electric Rail Energy Consumption Using the Lagrange Multiplier Technique." Journal of Transportation Engineering 139, no. 3 (March 2013): 321–29. http://dx.doi.org/10.1061/(asce)te.1943-5436.0000483.

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6

Sk, Nayem, and Abhik Kumar Sanyal. "On the equivalence between different canonical forms of F(R) theory of gravity." International Journal of Modern Physics D 27, no. 08 (May 30, 2018): 1850085. http://dx.doi.org/10.1142/s0218271818500852.

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Classical equivalence between Jordan’s and Einstein’s frame counterparts of [Formula: see text] theory of gravity has recently been questioned, since the two produce different Noether symmetries, which could not be translated back and forth using transformation relations. Here we add the Hamiltonian constraint equation, which is essentially the time–time component of Einstein’s equation, through a Lagrange multiplier to the existence condition for Noether symmetry and show that all the three different canonical structures of [Formula: see text] theory of gravity, including the one which follows from Lagrange multiplier technique, admit each and every available symmetry independently. This establishes classical equivalence.

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7

KHAN, NAWAB, QAZI MAHMOOD UL HASSAN, EHSAN UL HAQ, M. YAQUB KHAN, KAMRAN AYUB, and JAVERIYA AYUB. "ANALYTICAL TECHNIQUE WITH LAGRANGE MULTIPLIER FOR SOLVING SPECIFIC NONLINEAR DIFFERENTIAL EQUATIONS." Journal of Science and Arts 21, no. 1 (March 30, 2021): 5–14. http://dx.doi.org/10.46939/j.sci.arts-21.1-a01.

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This paper will use Lagrange parameter in Adomain decomposition method to suggest new method for solving nonlinear differential equation. This method will be highly order convergent. Also, this method will be compared with old existence method. At last, some numerical examples will be given to illustrate the efficiency of newly developed method.

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8

Negulescu, Claudia. "Mathematical Study of a Lagrange-Multiplier Technique for Stiff Transport Problems." Multiscale Modeling & Simulation 19, no. 2 (January 2021): 802–29. http://dx.doi.org/10.1137/20m1333717.

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9

Kuo, Way, Hsin-Hui Lin, Zhongkai Xu, and Weixing Zhang. "Reliability Optimization with the Lagrange-Multiplier and Branch-and-Bound Technique." IEEE Transactions on Reliability R-36, no. 5 (December 1987): 624–30. http://dx.doi.org/10.1109/tr.1987.5222487.

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10

Kanarska, Y., I. Lomov, and T. Antoun. "Mesoscale simulations of particulate flows with parallel distributed Lagrange multiplier technique." Computers & Fluids 48, no. 1 (September 2011): 16–29. http://dx.doi.org/10.1016/j.compfluid.2011.03.010.

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11

IRWANTO, B., H. J. HARDTKE, D. PAWANDENAT, and R. SCHMIDT. "ON SUBSTRUCTURING TECHNIQUE: APPLICATION OF LAGRANGE MULTIPLIER METHOD ON CYCLIC STRUCTURES." Journal of Sound and Vibration 247, no. 5 (November 2001): 939–45. http://dx.doi.org/10.1006/jsvi.2001.3683.

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12

Shah, Nehad Ali, S. Saleem, Ali Akgül, Kamsing Nonlaopon, and Jae Dong Chung. "Numerical Analysis of Time-Fractional Diffusion Equations via a Novel Approach." Journal of Function Spaces 2021 (May 26, 2021): 1–12. http://dx.doi.org/10.1155/2021/9945364.

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The aim of this paper is a new semianalytical technique called the variational iteration transform method for solving fractional-order diffusion equations. In the variational iteration technique, identifying of the Lagrange multiplier is an essential rule, and variational theory is commonly used for this purpose. The current technique has the edge over other methods as it does not need extra parameters and polynomials. The validity of the proposed method is verified by considering some numerical problems. The solution achieved has shown that the better accuracy of the proposed technique. This paper proposes a simpler method to calculate the multiplier using the Shehu transformation, making a valuable technique to researchers dealing with various linear and nonlinear problems.

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13

Lee, K. "Numerical analysis of dynamic contact with combined constraint of displacement, velocity and acceleration on the contact surface." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 216, no. 3 (March 1, 2002): 377–82. http://dx.doi.org/10.1243/0954406021524963.

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For an efficient dynamic contact analysis in finite element techniques, a contact error vector is defined on the possible contact surface by combining the displacement, velocity and acceleration, and the contact error vector is monotonically reduced by an iterative scheme similar to the augmented Lagrange multiplier method. The numerical experiments show that, when the time step size is small, the present technique gives more smooth and accurate solution than Abaqus.

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Alkahtani, Badr S., Vartika Gulati, and Pranay Goswami. "On the Solution of Generalized Space Time Fractional Telegraph Equation." Mathematical Problems in Engineering 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/861073.

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We present the solution of generalized space time fractional telegraph equation by using Sumudu variational iteration method which is the combination of variational iteration method and Sumudu transform. We tried to overcome the difficulties in finding the value of Lagrange multiplier by this new technique.

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15

Chomkwah, V., and X. J. R. Avula. "A high-order theory for laminated composite plates using lagrange multiplier technique." Computers & Structures 37, no. 5 (January 1990): 845–61. http://dx.doi.org/10.1016/0045-7949(90)90113-g.

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16

Катин, V. Katin, Косыгин, and V. Kosygin. "Technical and Economic Assessment of Protection Methods against Noise (as exemplified by the Noise of Refinery Furnaces’ Burner Units)." Safety in Technosphere 2, no. 3 (June 25, 2013): 70–74. http://dx.doi.org/10.12737/455.

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The technical and economic assessment of noise-protective actions is made during the operation of refinery furnaces’ burner units. The presented assessment technique is applicable to evaluation of protection measures against noise created by several sources. The assessment problem is solved with application of Lagrange multiplier method.

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17

Liu, Hongliang, Aiguo Xiao, and Lihong Su. "Convergence of Variational Iteration Method for Second-Order Delay Differential Equations." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/634670.

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This paper employs the variational iteration method to obtain analytical solutions of second-order delay differential equations. The corresponding convergence results are obtained, and an effective technique for choosing a reasonable Lagrange multiplier is designed in the solving process. Moreover, some illustrative examples are given to show the efficiency of this method.

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18

Alawad, Fatima A., Eltayeb A. Yousif, and Arbab I. Arbab. "A New Technique of Laplace Variational Iteration Method for Solving Space-Time Fractional Telegraph Equations." International Journal of Differential Equations 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/256593.

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In this paper, the exact solutions of space-time fractional telegraph equations are given in terms of Mittage-Leffler functions via a combination of Laplace transform and variational iteration method. New techniques are used to overcome the difficulties arising in identifying the general Lagrange multiplier. As a special case, the obtained solutions reduce to the solutions of standard telegraph equations of the integer orders.

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19

Mishima, Shigenori, and Spyros A. Kinnas. "A Numerical Optimization Technique Applied to the Design of Two-Dimensional Cavitating Hydrofoil Sections." Journal of Ship Research 40, no. 01 (March 1, 1996): 28–38. http://dx.doi.org/10.5957/jsr.1996.40.1.28.

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A numerical nonlinear optimization technique is applied to the systematic design of two-dimensional partially or supercavitating hydrofoil sections. The design objective is to minimize the hydrofoil drag for given lift and cavitation number. The hydrodynamic analysis of the cavitating hydrofoil is performed in nonlinear theory, via a low-order potential-based panel method. The effects of viscosity are taken into account via a uniform friction coefficient applied on the wetted foil surface. The total drag, lift, cavitation number, and other quantities involved in the imposed constraints, are expressed in terms of quadratic functions of the main parameters of the hydrofoil geometry, angle of attack, and the cavity length. The optimization is based on the method of multipliers by coupling the Lagrange multiplier terms and the penalty function terms. The robustness and convergence of the method are extensively investigated, and the results are compared with those from applying other design methods.

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20

Ma, Zheng-Dong, Noboru Kikuchi, Hsien-Chie Cheng, and Ichiro Hagiwara. "Topological Optimization Technique for Free Vibration Problems." Journal of Applied Mechanics 62, no. 1 (March 1, 1995): 200–207. http://dx.doi.org/10.1115/1.2895903.

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A topological optimization technique using the conception of OMD (Optimal Material Distribution) is presented for free vibration problems of a structure. A new objective function corresponding to multieigenvalue optimization is suggested for improving the solution of the eigenvalue optimization problem. An improved optimization algorithm is then applied to solve these problems, which is derived by the authors using a new convex generalized-linearization approach via a shift parameter which corresponds to the Lagrange multiplier and the use of the dual method. Finally, three example applications are given to substantiate the feasibility of the approaches presented in this paper.

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21

Cabanillas Lapa, Eugenio, and Willy Barahona Martinez. "On the Frictional Contact Problem of p(x)-Kirchhoff Type." International Journal of Analysis and Applications 20 (October 7, 2022): 52. http://dx.doi.org/10.28924/2291-8639-20-2022-52.

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In this article we consider a class of frictional contact problem of p(x)-Kirchhoff type, on a bounded domain Ω⊆R2. Using an abstract Lagrange multiplier technique and the Schauder’s fixed point theorem we establish the existence of weak solutions. Furthermore, we also obtain the uniqueness of the solution assuming that the datum f1 satisfies a suitable monotonicity condition.

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22

Mohyud-Din, Syed Tauseef, Muhammad Aslam Noor, and Khalida Inayat Noor. "Variational Iteration Method for Burgers’ and Coupled Burgers’ Equations Using He’s Polynomials." Zeitschrift für Naturforschung A 65, no. 4 (April 1, 2010): 263–67. http://dx.doi.org/10.1515/zna-2010-0401.

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In this paper, we apply a modified version of the variational iteration method (MVIM) for solving Burgers’ and coupled Burgers’ equations. The proposed modification is made by introducing He’s polynomials in the correction functional of the variational iteration method (VIM). The use of Lagrange multiplier coupled with He’s polynomials are the clear advantages of this technique over the decomposition method.

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23

Mohajan, Devajit, and Haradhan Kumar Mohajan. "The Responses of an Organization for the Increase in Wage Rates: Profit Maximization Cases." Law and Economy 2, no. 8 (August 2023): 14–29. http://dx.doi.org/10.56397/le.2023.08.02.

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Every organization expects to achieve maximum profit for its survival economic environment. To develop profit maximization strategy an organization must be sincere in economic sensitivity analysis. In this study sensitivity analysis is inspected to predict about the economic situation for the efficient production of the organization. Here scientific based production policy is indicated subject to a budget constraint, using Lagrange multiplier technique.

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24

Shateri, Majid, and D. D. Ganji. "Solitary Wave Solutions for a Time-Fraction Generalized Hirota-Satsuma Coupled KdV Equation by a New Analytical Technique." International Journal of Differential Equations 2010 (2010): 1–11. http://dx.doi.org/10.1155/2010/954674.

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A new iterative technique is employed to solve a system of nonlinear fractional partial differential equations. This new approach requires neither Lagrange multiplier like variational iteration method (VIM) nor polynomials like Adomian's decomposition method (ADM) so that can be more easily and effectively established for solving nonlinear fractional differential equations, and will overcome the limitations of these methods. The obtained numerical results show good agreement with those of analytical solutions. The fractional derivatives are described in Caputo sense.

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25

Kim, H. K., and Y.-S. Park. "An Efficient Response Analysis Method for a Non-Linear/Parameter Changing System Using Sub-Structure Modes." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 207, no. 1 (January 1993): 41–52. http://dx.doi.org/10.1243/pime_proc_1993_207_097_02.

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An efficient state-space method is presented to determine time domain forced responses of a structure using the Lagrange multiplier based sub-structure technique. Compared with the conventional mode synthesis methods, the suggested method can be particularly effective for the forced response analysis of a structure subjected to parameter changes with time, such as a missile launch system, and/or having localized non-linearities, because this method does not need to construct the governing equations of the combined whole structure. Both the loaded interface free-free modes and free interface modes can be employed as the modal bases of each sub-structure. The sub-structure equations of motion are derived using Lagrange multipliers and recurrence discrete-time state equations based upon the concept of the state transition matrix are formulated for transient response analysis. The suggested method is tested with two example structures, a simple lumped mass model with a non-linear joint and an abruptly parameter changing structure. The test results show that the suggested method is very accurate and efficient in calculating forced responses and in comparing it with the direct numerical integration method.

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Paz, E., F. Garcia-Sanchez, and O. Chubykalo-Fesenko. "Numerical evaluation of energy barriers in nano-sized magnetic elements with Lagrange multiplier technique." Physica B: Condensed Matter 403, no. 2-3 (February 2008): 330–33. http://dx.doi.org/10.1016/j.physb.2007.08.042.

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27

Seddighin, Morteza. "Optimally rotated vectors." International Journal of Mathematics and Mathematical Sciences 2003, no. 63 (2003): 4015–23. http://dx.doi.org/10.1155/s0161171203208334.

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We study vectors which undergo maximum or minimum rotation by a matrix on the field of real numbers. The cosine of the angle between a maximally rotated vector and its image under the matrix is called the cosine or antieigenvalue of the matrix and has important applications in numerical methods. Using Lagrange multiplier technique, we obtain systems of nonlinear equations which represent these optimization problems. Furthermore, we solve these systems symbolically and numerically.

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28

Zhang, Shiguang, Ting Zhou, Lin Sun, Wei Wang, Chuan Wang, and Wentao Mao. "ν-Support Vector Regression Model Based on Gauss-Laplace Mixture Noise Characteristic for Wind Speed Prediction." Entropy 21, no. 11 (October 28, 2019): 1056. http://dx.doi.org/10.3390/e21111056.

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Most regression techniques assume that the noise characteristics are subject to single noise distribution whereas the wind speed prediction is difficult to model by the single noise distribution because the noise of wind speed is complicated due to its intermittency and random fluctuations. Therefore, we will present the ν -support vector regression model of Gauss-Laplace mixture heteroscedastic noise (GLM-SVR) and Gauss-Laplace mixture homoscedastic noise (GLMH-SVR) for complex noise. The augmented Lagrange multiplier method is introduced to solve models GLM-SVR and GLMH-SVR. The proposed model is applied to short-term wind speed forecasting using historical data to predict future wind speed at a certain time. The experimental results show that the proposed technique outperforms the single noise technique and obtains good performance.

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29

K. Farhan, Marwa, and Muayad S. Croock. "D2D MULTI-OBJECTIVE ROUTE OPTIMIZATION IN MANET ENVIRONMENT." Iraqi Journal of Information and Communication Technology 5, no. 2 (August 22, 2022): 32–41. http://dx.doi.org/10.31987/ijict.5.2.199.

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Over the past decades, wireless networks and devices have experienced intensive growth. Route discovery and selection from device to device (D2D) that are randomly distributed came across services trade-offs. This paper presents an optimal routing technique for the MANET environment-based D2D network. The optimization method considers the Lagrange Multiplier approach to maximize bit rate along with constraints minimization of the latency and packet loss. This method is executed for D2D nodes by active route election for links. An intensive simulation is applied and the obtained simulation results manifest the effectiveness of the presented Lagrange Optimization of Rate, Delay, and Packet loss algorithm (LORDP) in the optimal routing as compared to the Particle Swarm Optimization (PSO) and Genetic Algorithm (GA).

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Kundu, B., and P. K. Das. "Performance Analysis and Optimization of Annular Fin With a Step Change in Thickness." Journal of Heat Transfer 123, no. 3 (October 26, 2000): 601–4. http://dx.doi.org/10.1115/1.1351165.

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The temperature distribution in a concentric annular fin with a step change in thickness (AFST) has been obtained analytically. The optimum design of such fins has been performed using Lagrange multiplier technique considering either the fin volume or the rate of heat transfer as the constraint. It has been demonstrated that the optimum AFSTs transfer more heat compared to optimum annular disc fins for a given fin volume as well as for given fin volume and fin length.

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Mohajan, Devajit, and Haradhan Kumar Mohajan. "Utility Maximization Analysis of an Organization: A Mathematical Economic Procedure." Law and Economy 2, no. 1 (January 2023): 1–15. http://dx.doi.org/10.56397/le.2023.01.01.

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In the society utility is the vital concept, especially in mathematical economics. It is considered as the tendency of an object or action that increases or decreases overall happiness. In social sciences, the property of a commodity that enables to satisfy human wants is called utility. This paper has tried to operate utility maximization policy of an organization by considering two constraints: budget constraint and coupon constraint. To develop the maximization policy of utility function, the techniques of multivariate calculus are used. In this study four commodity variables are used to operate the mathematical analysis efficiently. In this article Lagrange multiplier technique is applied to achieve optimal result throughout the study.

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Zhang, Haiyong, Dong Han, Kai Ji, Zhong Ren, Chi Xu, Lijuan Zhu, and Hongyan Tan. "Optimal Spatial Matrix Filter Design for Array Signal Preprocessing." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/564976.

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An efficient technique of designing spatial matrix filter for array signal preprocessing based on convex programming was proposed. Five methods were considered for designing the filter. In design method 1, we minimized the passband fidelity subject to the controlled overall stopband attenuation level. In design method 2, the objective function and the constraint in the design method 1 were reversed. In design method 3, the optimal matrix filter which has the general mean square error was considered. In design method 4, the left stopband and the right stopband were constrained with specific attenuation level each, and the minimized passband fidelity was received. In design method 5, the optimization objective function was the sum of the left stopband and the right stopband attenuation levels with the weighting factors 1 andγ, respectively, and the passband fidelity was the constraints. The optimal solution of the optimizations above was derived by the Lagrange multiplier theory. The relations between the optimal solutions were analyzed. The generalized singular value decomposition was introduced to simplify the optimal solution of design methods 1 and 2 and enhanced the efficiency of solving the Lagrange multipliers. By simulations, it could be found that the proposed method was effective for designing the spatial matrix filter.

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Flocker, Forrest W. "Controlling the Frequency Content of Inertia Forces in Dwelling Cam-Follower Systems." Journal of Mechanical Design 129, no. 5 (May 12, 2006): 546–52. http://dx.doi.org/10.1115/1.2712222.

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Background. Cam-driven machines are frequently manufactured with the intent that they be installed in many different end applications, each with its own natural frequencies. A cam-driven component that performs well in one end application can excite obnoxious or damaging vibrations in another. Method of Approach. A Lagrange multiplier technique is presented that optimally modifies follower motion such that unwanted inertia force frequencies are suppressed. Results. An example problem illustrates the method and presents results. Conclusions. The technique provides a robust customization procedure, permitting the use of a cam-driven component in a wider variety of end applications.

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Mohajan, Devajit, and Haradhan Kumar Mohajan. "An Economical Study When Cost of Irregular Raw Materials of an Industry Increases for Nonlinear Budget Constraint." Law and Economy 2, no. 7 (July 2023): 24–43. http://dx.doi.org/10.56397/le.2023.07.04.

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Very few researches try to work with nonlinear budget constraint. This study attempts to discuss the sensitivity analysis with the use of nonlinear budget constraint. For the efficient use of inputs every industry should inspects economic analysis for the profit maximization. In this study Lagrange multiplier technique is applied with the bordered Hessian and Jacobian. For the sustainability of an industry in the competitive global economy, the industry should proceed through the application of scientific method, such as application of optimization policy.

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Mohajan, Devajit, and Haradhan Kumar Mohajan. "Sensitivity Analysis of Inputs of an Organization: A Profit Maximization Exploration." Law and Economy 2, no. 4 (April 2023): 32–48. http://dx.doi.org/10.56397/le.2023.04.06.

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This article tries to discuss sensitivity analysis of various inputs of an organization during profit maximization investigations. In this study Cobb-Douglas production function is analyzed with a detail mathematical analysis. The method of Lagrange multiplier is a very useful and powerful technique in multivariate calculus, and it is applied here to obtain higher dimensional unconstrained problem from the lower dimensional constrained one. In the article determinant of the 6×6 bordered Hessian matrix and 6×6 Jacobian are operated for consulting sensitivity analysis efficiently.

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Sawanobori, Hisaki, and Mutsuto Kawahara. "Optimal Control of an Oscillating Body Using the Adjoint Equation and ALE Finite Element Methods." Advanced Materials Research 403-408 (November 2011): 5102–6. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.5102.

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The purpose of this study is to determine the optimal angle of wings which is attached to an oscillating body located in an incompressible flow. At present, there are some bridges with wings to prevent oscillation by the wind. The angle of the wing is very important so as to minimize the oscillation of bridge. In this study, the angle to minimize the oscillation is presented by optimal control theory. In order to minimize the oscillation, the performance function which is expressed by the displacement of body is introduced. The performance function should be minimized satisfying state equation. This problem can be transformed into the minimization problem by the Lagrange multiplier method. As a minimization technique, the weighted gradient method is applied. For the discretization, the arbitrary Lagrangan-Eulerian(ALE) finite element method is applied to solve the FSI problem. The optimal control of an oscillating bridge is shown as numerical study.

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Santos, Antônio José Boness, C. O. Faria, and Abimael F. D. Loula. "A Stabilized Hybrid Discontinuous Galerkin Method for Nearly Incompressible Linear Elasticity Problem." TEMA (São Carlos) 18, no. 3 (January 10, 2018): 467. http://dx.doi.org/10.5540/tema.2017.018.03.467.

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In this work, a primal hybrid finite element method for nearly incom pressible linear elasticity problem on triangular meshes is shown. This method consists of coupling local discontinuous Galerkin problems to the primal variable with a global problem for the Lagrange multiplier, which is identified as the trace of the displacement field. Also, a local post-processing technique is used to recover stress approximations with improved rates of convergence in H(div) norm. Numerical studies show that the method is locking free even using equal or different orders for displacement and stress fields and optimal convergence rates are obtained.

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Ilyas, Muhammad, Agah D. Garnadi, and Sri Nurdiati. "Adaptive Mixed Finite Element Method for Elliptic Problems with Concentrated Source Terms." Indonesian Journal of Science and Technology 4, no. 2 (July 9, 2019): 263–69. http://dx.doi.org/10.17509/ijost.v4i2.18183.

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An adaptive mixed finite element method using the Lagrange multiplier technique is used to solve elliptic problems with delta Dirac source terms. The problem arises in the use of Chow-Anderssen linear functional methodology to recover coefficients locally in parameter estimation of an elliptic equation from a point-wise measurement. In this article, we used a posterior error estimator based on averaging technique as refinement indicators to produce a cycle of mesh adaptation, which is experimentally shown to capture singularity phenomena. Our numerical results showed that the adaptive refinement process successfully refines elements around the center of the source terms. The results also showed that the global error estimation is better than uniform refinement process in terms of computation time.

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AHMAD, ABRAR, QUAZZAFI RABBANI, and A. H. ANSARI. "DETERMINATION OF OPTIMUM SAMPLE SIZE AND VARIANCE IN MULTIVARIATE STRATIFIED SAMPLING WITH NON-LINEAR TIME FUNCTION." Journal of Science and Arts 23, no. 2 (June 30, 2023): 513–24. http://dx.doi.org/10.46939/j.sci.arts-23.2-a18.

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Stratified sample size which determined in Stratified Random Sampling (SRS) with the help of different allocation techniques. The multivariate stratified sampling with linear or nonlinear time function can be optimized using generalized model of time function. After formulation as generalized model with time function (linear or nonlinear), in which the information given that there is only one varying time (time of transportation) and different time involved are constants or insignificant. The formulated generalized model was solved using different techniques but in present paper we use Lagrange multiplier technique to get the optimal solution (i.e. by minimizing the variance) with the involved time constraints. The generalized model with time of transportation is derived under optimum allocation and other involved time is fixed, when the sample size and its variances for a given time is unknown, then different allocation techniques are required for proportionality constant and a given time.

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Chen, Qiwei, Cheng Wu, and Yiming Wang. "Robust Principal Component Analysis-Based Infrared Small Target Detection." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 9925–26. http://dx.doi.org/10.1609/aaai.v33i01.33019925.

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A method based on Robust Principle Component Analysis (RPCA) technique is proposed to detect small targets in infrared images. Using the low rank characteristic of background and the sparse characteristic of target, the observed image is regarded as the sum of a low-rank background matrix and a sparse outlier matrix, and then the decomposition is solved by the RPCA. The infrared small target is extracted from the single-frame image or multi-frame sequence. In order to get more efficient algorithm, the iteration process in the augmented Lagrange multiplier method is improved. The simulation results show that the method can detect out the small target precisely and efficiently.

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Sabila, Fadiyah Hani. "Stock Selection dan Market Timing Ability Reksa Dana Syariah Saham di Indonesia." Journal of Economic, Public, and Accounting (JEPA) 1, no. 2 (April 26, 2019): 68–81. http://dx.doi.org/10.31605/jepa.v1i2.275.

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The purpose of this research is to know investment manager’s ability on stock selection and market timing of Indonesia sharia equity mutual funds on 2015-2017. Number of sample that use in this research is 15 sample with purposive sampling method. Data analysis technique used is Treynor-Mazuy condition regression model using panel data. This research method using panel data analysis test that is test Chow, Hausman, and Lagrange Multiplier. The result showed that the model chosen is a random effect models. F test and T test results indicate that investment manager’s of Indonesia sharia equity mutual funds have stock selection and market timing ability.

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Won, Kwang-Min, and Youn-sik Park. "Eigenvalue Sensitivity Analysis for a Combined Beam Structure with Varying Constraints." Shock and Vibration 4, no. 5-6 (1997): 341–50. http://dx.doi.org/10.1155/1997/432457.

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An eigenvalue sensitivity formula for a combined beam structure due to the variation of its shape or joint coordinates is proposed based on the Lagrange multiplier technique for a free vibration equation of the structure. The shape variation is decomposed into the length and the orientation variation of each beam to obtain individual effects on the total sensitivity. The sensitivity equations due to the length and the orientation variations are expressed as an energy density form and the cross product of joint forces and displacements respectively. Several numerical examples are also presented to validate the proposed formulation and to show how to implement the idea.

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Golbabai, Ahmad, Nima Safaei, and Mahboubeh Molavi-Arabshahi. "Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method." Entropy 24, no. 10 (September 23, 2022): 1345. http://dx.doi.org/10.3390/e24101345.

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This paper introduces a direct method derived from the global radial basis function (RBF) interpolation over arbitrary collocation nodes occurring in variational problems involving functionals that depend on functions of a number of independent variables. This technique parameterizes solutions with an arbitrary RBF and transforms the two-dimensional variational problem (2DVP) into a constrained optimization problem via arbitrary collocation nodes. The advantage of this method lies in its flexibility in selecting between different RBFs for the interpolation and parameterizing a wide range of arbitrary nodal points. Arbitrary collocation points for the center of the RBFs are applied in order to reduce the constrained variation problem into one of a constrained optimization. The Lagrange multiplier technique is used to transform the optimization problem into an algebraic equation system. Three numerical examples indicate the high efficiency and accuracy of the proposed technique.

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El-Arini, Mahdi M. M., Ahmed M. Othman, and Ahmed Fathy. "A New Optimization Approach for Maximizing the Photovoltaic Panel Power Based on Genetic Algorithm and Lagrange Multiplier Algorithm." International Journal of Photoenergy 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/481468.

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In recent years, the solar energy has become one of the most important alternative sources of electric energy, so it is important to operate photovoltaic (PV) panel at the optimal point to obtain the possible maximum efficiency. This paper presents a new optimization approach to maximize the electrical power of a PV panel. The technique which is based on objective function represents the output power of the PV panel and constraints, equality and inequality. First the dummy variables that have effect on the output power are classified into two categories: dependent and independent. The proposed approach is a multistage one as the genetic algorithm, GA, is used to obtain the best initial population at optimal solution and this initial population is fed to Lagrange multiplier algorithm (LM), then a comparison between the two algorithms, GA and LM, is performed. The proposed technique is applied to solar radiation measured at Helwan city at latitude 29.87°, Egypt. The results showed that the proposed technique is applicable.

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Derakhshan, MohammadHossein. "New Numerical Algorithm to Solve Variable-Order Fractional Integrodifferential Equations in the Sense of Hilfer-Prabhakar Derivative." Abstract and Applied Analysis 2021 (February 24, 2021): 1–10. http://dx.doi.org/10.1155/2021/8817794.

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In this article, a numerical technique based on the Chebyshev cardinal functions (CCFs) and the Lagrange multiplier technique for the numerical approximation of the variable-order fractional integrodifferential equations are shown. The variable-order fractional derivative is considered in the sense of regularized Hilfer-Prabhakar and Hilfer-Prabhakar fractional derivatives. To solve the problem, first, we obtain the operational matrix of the regularized Hilfer-Prabhakar and Hilfer-Prabhakar fractional derivatives of CCFs. Then, this matrix and collocation method are used to reduce the solution of the nonlinear coupled variable-order fractional integrodifferential equations to a system of algebraic equations which is technically simpler for handling. Convergence and error analysis are examined. Finally, some examples are given to test the proposed numerical method to illustrate its accuracy and efficiency.

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Marpaung, Riky Aulia Rachman, Iin Sintia, and Fitri Rahayu. "Analysis of the Effect of Open Unemployment Rate and Human Development Index on Poverty in North Sumatra Province." Indonesian Journal of Advanced Research 2, no. 5 (May 31, 2023): 361–76. http://dx.doi.org/10.55927/ijar.v2i5.4141.

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This study aims to determine the effect of the Open Unemployment Rate and the Human Development Index on poverty in North Sumatra. The data used is secondary data taken from BPS concerning the open unemployment rate, human development index and poverty percentage. Data obtained from panel data from 33 regencies/cities in North Sumatra for 3 years from 2020 to 2022. The data analysis technique uses regression analysis using Random Effect based on the results of the Lagrange Multiplier test. The results of the study show that the open unemployment rate has a negative and insignificant effect on poverty. Meanwhile, the human development index has a negative and significant effect on poverty in North Sumatra.

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Zhang, Yan, Yonghong Wu, and Haixiang Yao. "Optimal Insurance Indemnity and Reinsurance Strategy for Health Insurance." Mathematical Problems in Engineering 2021 (August 13, 2021): 1–13. http://dx.doi.org/10.1155/2021/3931230.

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“Health insurance + health management” package has recently become one of the most important nonlife insurance products, and its pricing technique has drawn attention from both academia and industry. This paper investigates the optimal indemnity design and per-loss reinsurance strategy for the health insurance package, where the reinsurance contract is assumed to combine the quota-share type and the excess-of-loss type. By applying the Lagrange multiplier method and optimal control technique, we develop the solutions to the corresponding optimization problems and obtain the optimal deductible. Then, we proceed to solve the optimal quota-share proportion and the optimal stop-loss retention based on the optimal insurance indemnity. In addition to theoretical results, numerical examples are also given to illustrate the effects of various key parameters on the optimal indemnity design and combinational reinsurance strategy.

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Rahimi, Esmaeil, Kazem Oraee, Zia Aldin Shafahi, and Hasan Ghasemzadeh. "Determining the Optimum Cut-Off Grades in Sulfide Copper Deposits / Określanie Optymalnej Wartości Odcięcia Zawartości Procentowej Pierwiastka Użytecznego W Złożach Siarczku Miedzi." Archives of Mining Sciences 60, no. 1 (March 1, 2015): 313–28. http://dx.doi.org/10.1515/amsc-2015-0021.

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Abstract Optimum cut-off grades determination in mining life affects production planning and ultimate pit limit and it is also important from social, economical and environmental aspects. Calculation of optimum cut-off grades has been less considered for mines containing various mineral processing methods. In this paper, an optimization technique is applied to obtain optimum cut-off grades for both concentration and heap leaching processes. In this technique, production costs and different recoveries of heap leaching method directed into modeling different annual cash flows in copper mines. Considering the governing constraints, the Lagrange multiplier method is practiced to optimize the cut-off grades in which the objective function is supposed to maximize Net Present Value. The results indicate the effect of heap leaching process on the optimum cut-off grades of primary and secondary sulfide deposits.

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Li, Xiang Qian, Wei Wei Wang, Ming Hai Li, and Mao Yu Zhen. "Meshless Element-Free Galerkin Method for Ground-Coupled Heat Transfer Problems." Applied Mechanics and Materials 263-266 (December 2012): 3292–97. http://dx.doi.org/10.4028/www.scientific.net/amm.263-266.3292.

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A meshless element-free Galerkin method (EFGM) which is applicable to arbitrary shapes but requires only nodal data is applied to two-dimensional steady-state ground-coupled heat transfer problems. The soil layer around underground constructions is modeled as a homogeneous medium and as a layered soil with two layers. Variational method is utilized to obtain the discrete equations. Moving least squares (MLS) approximants are used to construct the shape functions. Lagrange multiplier technique is employed to enforce the essential boundary conditions. The calculation precision of EFGM is validated by comparing EFGM results with those obtained by finite element method (FEM). EFGM reduce considerably the preparation of the model. EFGM is very appropriate for the ground-coupled heat transfer problems.

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Zhong, Zhi Peng, Shui Wan, and Lin Yun Zhou. "A new Interface Element Method on Computation of the Interface Crack Propagation Energy Release Rate." Applied Mechanics and Materials 204-208 (October 2012): 4573–77. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.4573.

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A new interface element method was proposed to calculate the strain energy release rates(SERR) based on the virtual crack closure technique (VCCT). A Lagrange multiplier was introduced between the node pair at crack tip to obtain the internal forces. Then from the VCCT, the SERR was solved by using the forces and displacements near the crack tip. Examples for stationary cracks under the two typical cases are given. Meanwhile, the relationship curves between crack energy release rate and the length of crack, plate depths were plotted respectively.The example shows that the interface element used to calculate the SERR is simple, efficient, and highly accurate in analysis of 2D crack growth problems, and without requiring the special singularity element or collapsed element at crack tip.

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