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Journal articles on the topic 'Variational problem'

Author: Grafiati

Published: 14 March 2023

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1

Palese, Marcella. "Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currents." Communications in Mathematics 24, no. 2 (December 1, 2016): 125–35. http://dx.doi.org/10.1515/cm-2016-0009.

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Abstract We will pose the inverse problem question within the Krupka variational sequence framework. In particular, the interplay of inverse problems with symmetry and invariance properties will be exploited considering that the cohomology class of the variational Lie derivative of an equivalence class of forms, closed in the variational sequence, is trivial. We will focalize on the case of symmetries of globally defined field equations which are only locally variational and prove that variations of local Noether strong currents are variationally equivalent to global canonical Noether currents. Variations, taken to be generalized symmetries and also belonging to the kernel of the second variational derivative of the local problem, generate canonical Noether currents - associated with variations of local Lagrangians - which in particular turn out to be conserved along any section. We also characterize the variation of the canonical Noether currents associated with a local variational problem.

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2

Hua, Yuan, Bao Hua Lv, and Tai Quan Zhou. "Parametric Variational Principle for Solving Coupled Damage Problem." Key Engineering Materials 348-349 (September 2007): 813–16. http://dx.doi.org/10.4028/www.scientific.net/kem.348-349.813.

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The parametric variational principle adopts the extreme variational idea in the modern control theory and uses state equations deduced from the constitutive law to control the functional variation, which is an effective solution to the nonlinear equations. Based on the fundamental equations of elasto-plasticity coupled damage problem, the potential functional of elasto-plasticity is constructed. Also the state equations with approximation of damage evolution equation and load functions are constructed in the paper. The solution of elasto-plasticity damage problem can be deduced to solve problem of the minimum potential energy function under the restriction of state equations. Thus the parametric variational principle for coupled damage is proposed. The variational principle has the virtue of definite physical meaning and the finite element equations are presented in the article to facilitate the application of parametric variatioal principle, which is easy to program on computer. Using the method mentioned in the article, a numerical calculation is carried out and the calculation result shows that the method is efficient for solving elasto-plasticity damage problem.

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3

Garg, Anupam. "Two variational variations on a problem in electrostatics." American Journal of Physics 75, no. 6 (June 2007): 509–12. http://dx.doi.org/10.1119/1.2717220.

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4

Zorii, N. V. "Extremal problems dual to the Gauss variational problem." Ukrainian Mathematical Journal 58, no. 6 (June 2006): 842–61. http://dx.doi.org/10.1007/s11253-006-0108-3.

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5

Bistafa, Sylvio R. "Euler's Navigation Variational Problem." Euleriana 2, no. 2 (September 19, 2022): 131. http://dx.doi.org/10.56031/2693-9908.1045.

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6

Onofri, E. "A Nonlinear Variational Problem." SIAM Review 27, no. 4 (December 1985): 576–78. http://dx.doi.org/10.1137/1027155.

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7

Cruz, Fátima, Ricardo Almeida, and Natália Martins. "Herglotz Variational Problems Involving Distributed-Order Fractional Derivatives with Arbitrary Smooth Kernels." Fractal and Fractional 6, no. 12 (December 10, 2022): 731. http://dx.doi.org/10.3390/fractalfract6120731.

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In this paper, we consider Herglotz-type variational problems dealing with fractional derivatives of distributed-order with respect to another function. We prove necessary optimality conditions for the Herglotz fractional variational problem with and without time delay, with higher-order derivatives, and with several independent variables. Since the Herglotz-type variational problem is a generalization of the classical variational problem, our main results generalize several results from the fractional calculus of variations. To illustrate the theoretical developments included in this paper, we provide some examples.

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8

Parida, J., M. Sahoo, and A. Kumar. "A variational-like inequality problem." Bulletin of the Australian Mathematical Society 39, no. 2 (April 1989): 225–31. http://dx.doi.org/10.1017/s0004972700002690.

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Given a closed and convex set K in Rn and two continuous maps F: K → Rn and η: K × K → Rn, the problem considered here is to find ε K such that.We call it a variational-like inequality problem, and develop a theory for the existence of a solution. We also show the relationship between the variational-like inequality problem and some mathematical programming problems.

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9

Jha, Shalini, Prasun Das, and Tadeusz Antczak. "Exponential type duality for η-approximated variational problems." Yugoslav Journal of Operations Research 30, no. 1 (2020): 19–43. http://dx.doi.org/10.2298/yjor190415022j.

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In this article, we use the so-called ?-approximation method for solving a new class of nonconvex variational problems with exponential (p, r)-invex functionals. In this approach, we construct ?-approximated variational problem and ?-approximated Mond- Weir dual variational problem for the considered variational problem and its Mond-Weir dual variational problem. Then several duality results for considered variational problem and its Mond-Weir dual variational problem are proved by the help of duality results established between ?-approximated variational problems mentioned above.

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10

Bock, Igor, and Ján Lovíšek. "An optimal control problem for a pseudoparabolic variational inequality." Applications of Mathematics 37, no. 1 (1992): 62–80. http://dx.doi.org/10.21136/am.1992.104492.

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11

Zhao, Yali, and Dongxue Han. "Split General Strong Nonlinear Quasi-Variational Inequality Problem." Mathematical Problems in Engineering 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/5937016.

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We introduce a split general strong nonlinear quasi-variational inequality problem which is a natural extension of a split general quasi-variational inequality problem, split variational inequality problem, and quasi-variational and variational inequality problems in Hilbert spaces. Using the projection method, we propose an iterative algorithm for the split general strongly nonlinear quasi-variational inequality problem and discuss the convergence criteria of the iterative algorithm. The results presented here generalized, unify, and improve many previously known results for quasi-variational and variational inequality problems.

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12

Baiz, Othmane, Hicham Benaissa, Rachid Bouchantouf, and Driss El Moutawakil. "OPTIMIZATION PROBLEMS FOR A THERMOELASTIC FRICTIONAL CONTACT PROBLEM." Mathematical Modelling and Analysis 26, no. 3 (September 10, 2021): 444–68. http://dx.doi.org/10.3846/mma.2021.12803.

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In the present paper, we analyze and study the control of a static thermoelastic contact problem. We consider a model which describes a frictional contact problem between a thermoelastic body and a deformable heat conductor obstacle. We derive a variational formulation of the model which is in the form of a coupled system of the quasi-variational inequality of elliptic type for the displacement and the nonlinear variational equation for the temperature. Then, under a smallness assumption, we prove the existence of a unique weak solution to the problem. Moreover, we establish the dependence of the solution with respect to the data and prove a convergence result. Finally, we introduce an optimization problem related to the contact model for which we prove the existence of a minimizer and provide a convergence result.

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13

Moreno, Giovanni, and Monika Ewa Stypa. "Geometry of the free-sliding Bernoulli beam." Communications in Mathematics 24, no. 2 (December 1, 2016): 153–71. http://dx.doi.org/10.1515/cm-2016-0011.

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Abstract If a variational problem comes with no boundary conditions prescribed beforehand, and yet these arise as a consequence of the variation process itself, we speak of the free boundary values variational problem. Such is, for instance, the problem of finding the shortest curve whose endpoints can slide along two prescribed curves. There exists a rigorous geometric way to formulate this sort of problems on smooth manifolds with boundary, which we review here in a friendly self-contained way. As an application, we study the particular free boundary values variational problem of the free-sliding Bernoulli beam.

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14

Chaloemyotphong, Bunyawee, and Atid Kangtunyakarn. "Modified Halpern Iterative Method for Solving Hierarchical Problem and Split Combination of Variational Inclusion Problem in Hilbert Space." Mathematics 7, no. 11 (November 3, 2019): 1037. http://dx.doi.org/10.3390/math7111037.

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The purpose of this paper is to introduce the split combination of variational inclusion problem which combines the concept of the modified variational inclusion problem introduced by Khuangsatung and Kangtunyakarn and the split variational inclusion problem introduced by Moudafi. Using a modified Halpern iterative method, we prove the strong convergence theorem for finding a common solution for the hierarchical fixed point problem and the split combination of variational inclusion problem. The result presented in this paper demonstrates the corresponding result for the split zero point problem and the split combination of variation inequality problem. Moreover, we discuss a numerical example for supporting our result and the numerical example shows that our result is not true if some conditions fail.

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15

Bakaryan, Tigran, Rita Ferreira, and Diogo Gomes. "A potential approach for planning mean-field games in one dimension." Communications on Pure and Applied Analysis 21, no. 6 (2022): 2147. http://dx.doi.org/10.3934/cpaa.2022054.

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<p style='text-indent:20px;'>This manuscript discusses planning problems for first- and second-order one-dimensional mean-field games (MFGs). These games are comprised of a Hamilton–Jacobi equation coupled with a Fokker–Planck equation. Applying Poincaré's Lemma to the Fokker–Planck equation, we deduce the existence of a potential. Rewriting the Hamilton–Jacobi equation in terms of the potential, we obtain a system of Euler–Lagrange equations for certain variational problems. Instead of the mean-field planning problem (MFP), we study this variational problem. By the direct method in the calculus of variations, we prove the existence and uniqueness of solutions to the variational problem. The variational approach has the advantage of eliminating the continuity equation.</p><p style='text-indent:20px;'>We also consider a first-order MFP with congestion. We prove that the congestion problem has a weak solution by introducing a potential and relying on the theory of variational inequalities. We end the paper by presenting an application to the one-dimensional Hughes' model.</p>

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16

Egorshin, A. O. "On one variational smoothing problem." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, no. 4 (December 2011): 9–22. http://dx.doi.org/10.20537/vm110402.

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17

Malozemov, Vassili N., and Grigoriy Sh Tamasyan. "On a cubic variational problem." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 3(61), no. 4 (2016): 615–23. http://dx.doi.org/10.21638/11701/spbu01.2016.410.

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18

BOGOLUBOV, N. N., A. N. KIREEV, and A. M. KURBATOV. "VARIATIONAL APPROACH TO POLARON PROBLEM." International Journal of Modern Physics B 01, no. 01 (April 1987): 89–102. http://dx.doi.org/10.1142/s0217979287000074.

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Variational Ansatz to describe the ground state of Fröhlich’s Polaron at all interaction strength is proposed. The best upper bounds to the polaron ground state energy are obtained in the limiting cases of weak and strong interactions. For intermediate couplings two simple models are investigated. The ground state energy does not exceed their minimal solution.

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19

Schmidt, Bernd. "On a semilinear variational problem." ESAIM: Control, Optimisation and Calculus of Variations 17, no. 1 (October 9, 2009): 86–101. http://dx.doi.org/10.1051/cocv/2009038.

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20

Malozemov, V. N., and G. Sh Tamasyan. "On a cubic variational problem." Vestnik St. Petersburg University: Mathematics 49, no. 4 (October 2016): 350–58. http://dx.doi.org/10.3103/s1063454116040105.

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21

Egorov, Yu V. "On one variational Butkovskii problem." Automation and Remote Control 73, no. 8 (August 2012): 1301–4. http://dx.doi.org/10.1134/s0005117912080036.

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22

Henriques, Pedro Gonçalves. "Inverse Problem of Variational Calculus." São Paulo Journal of Mathematical Sciences 5, no. 2 (December 30, 2011): 233. http://dx.doi.org/10.11606/issn.2316-9028.v5i2p233-248.

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23

Kazmi, Kaleem. "Split nonconvex variational inequality problem." Mathematical Sciences 7, no. 1 (2013): 36. http://dx.doi.org/10.1186/2251-7456-7-36.

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24

Lorz, Alexander, Peter Markowich, and Benoît Perthame. "Bernoulli Variational Problem and Beyond." Archive for Rational Mechanics and Analysis 212, no. 2 (December 17, 2013): 415–43. http://dx.doi.org/10.1007/s00205-013-0707-8.

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25

Saunders, David J. "Jets and the variational calculus." Communications in Mathematics 29, no. 1 (April 30, 2021): 91–114. http://dx.doi.org/10.2478/cm-2021-0004.

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Abstract We review the approach to the calculus of variations using Ehresmann’s theory of jets. We describe different types of jet manifold, different types of variational problem and different cohomological structures associated with such problems.

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26

Garaev, K. G., and L. A. Aksent’ev. "A problem on brachistochrone as invariant variational problem." Russian Mathematics 61, no. 1 (January 2017): 81–84. http://dx.doi.org/10.3103/s1066369x17010108.

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27

FRANCAVIGLIA, MAURO, MARCELLA PALESE, and EKKEHART WINTERROTH. "VARIATIONALLY EQUIVALENT PROBLEMS AND VARIATIONS OF NOETHER CURRENTS." International Journal of Geometric Methods in Modern Physics 10, no. 01 (November 15, 2012): 1220024. http://dx.doi.org/10.1142/s0219887812200241.

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We consider systems of local variational problems defining nonvanishing cohomology classes. Symmetry properties of the Euler–Lagrange expressions play a fundamental role since they introduce a cohomology class which adds up to Noether currents; they are related with invariance properties of the first variation, thus with the vanishing of a second variational derivative. In particular, we prove that the conserved current associated with a generalized symmetry, assumed to be also a symmetry of the variation of the corresponding local inverse problem, is variationally equivalent to the variation of the strong Noether current for the corresponding local system of Lagrangians. This current is conserved and a sufficient condition will be identified in order that such a current be global.

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28

Jha, Shalini, Prasun Das, and Sanghamitra Bandhyopadhyay. "Multitime multiobjective variational problems via η-approximation method." Yugoslav Journal of Operations Research, no. 00 (2021): 15. http://dx.doi.org/10.2298/yjor201115015j.

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The present article is devoted to multitime multiobjective variational problems via ?-approximation method. In this method, an ?-approximation approach is applied to the considered problem, and a new problem is constructed, called as ?-approximated multitime multiobjective variational problem that contains the change in objective and both constraints functions. The equivalence between an efficient (Pareto optimal) solution to the main multitime multiobjective variational problem is derived along with its associated ?-approximated problem under invexity defined for a multi- time functional. Furthermore, we have also discussed the saddle-point criteria for the problem considered and its associated ?-approximated problems via generalized invexity assumptions.

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29

Zhang, Yi. "Noether's symmetry and conserved quantity for a time-delayed Hamiltonian system of Herglotz type." Royal Society Open Science 5, no. 10 (October 2018): 180208. http://dx.doi.org/10.1098/rsos.180208.

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The variational problem of Herglotz type and Noether's theorem for a time-delayed Hamiltonian system are studied. Firstly, the variational problem of Herglotz type with time delay in phase space is proposed, and the Hamilton canonical equations with time delay based on the Herglotz variational problem are derived. Secondly, by using the relationship between the non-isochronal variation and the isochronal variation, two basic formulae of variation of the Hamilton–Herglotz action with time delay in phase space are derived. Thirdly, the definition and criterion of the Noether symmetry for the time-delayed Hamiltonian system are established and the corresponding Noether's theorem is presented and proved. The theorem we obtained contains Noether's theorem of a time-delayed Hamiltonian system based on the classical variational problem and Noether's theorem of a Hamiltonian system based on the variational problem of Herglotz type as its special cases. At the end of the paper, an example is given to illustrate the application of the results.

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30

Garzon, Gabriel Ruiz. "The Pre-Variational Problems and the Constrained Mathematical Programming Problem." OPSEARCH 39, no. 2 (June 2002): 63–75. http://dx.doi.org/10.1007/bf03398671.

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31

Ceng, Lu-Chuan, Chi-Ming Chen, Ching-Feng Wen, and Chin-Tzong Pang. "Relaxed Iterative Algorithms for Generalized Mixed Equilibrium Problems with Constraints of Variational Inequalities and Variational Inclusions." Abstract and Applied Analysis 2014 (2014): 1–25. http://dx.doi.org/10.1155/2014/345212.

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We introduce and analyze a relaxed extragradient-like viscosity iterative algorithm for finding a solution of a generalized mixed equilibrium problem with constraints of several problems: a finite family of variational inequalities for inverse strongly monotone mappings, a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings, and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some suitable conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution of these problems which also solves a variational inequality problem.

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32

Kheawborisut, Araya, and Atid Kangtunyakarn. "Algorithms of common solutions to modified generalized system of variational inclusion problem and hierarchical fixed point problem." Filomat 36, no. 9 (2022): 3173–88. http://dx.doi.org/10.2298/fil2209173k.

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This manuscript deals with two problems : the first one is a new problem of the system of variational inclusion that is called modified generalized system of variational inclusion problem(MGSVIP) and the other one is a hierarchical fixed point problem in the framework of real Hilbert space. We establish the important lemma that show the relation between fixed point of nonlinear mapping and solution of MGSVIP for proving the main theorem. To approximate the common solution of these problems, we design an iterative scheme under suitable conditions on parameters. A strong convergence result for the proposed iterative scheme is proved. Applying our main result, we prove strong convergence theorems of the modification system of variational inequalities problem and variational inclusion problem. Moreover, we give the numerical example for supporting our results.

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33

Farajzadeh, A. P., and B. S. Lee. "Vector variational-like inequality problem and vector optimization problem." Applied Mathematics Letters 23, no. 1 (January 2010): 48–52. http://dx.doi.org/10.1016/j.aml.2009.07.024.

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34

KAWOHL, BERND, and FRIEDEMANN SCHURICHT. "DIRICHLET PROBLEMS FOR THE 1-LAPLACE OPERATOR, INCLUDING THE EIGENVALUE PROBLEM." Communications in Contemporary Mathematics 09, no. 04 (August 2007): 515–43. http://dx.doi.org/10.1142/s0219199707002514.

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We consider a number of problems that are associated with the 1-Laplace operator Div (Du/|Du|), the formal limit of the p-Laplace operator for p → 1, by investigating the underlying variational problem. Since corresponding solutions typically belong to BV and not to [Formula: see text], we have to study minimizers of functionals containing the total variation. In particular we look for constrained minimizers subject to a prescribed [Formula: see text]-norm which can be considered as an eigenvalue problem for the 1-Laplace operator. These variational problems are neither smooth nor convex. We discuss the meaning of Dirichlet boundary conditions and prove existence of minimizers. The lack of smoothness, both of the functional to be minimized and the side constraint, requires special care in the derivation of the associated Euler–Lagrange equation as necessary condition for minimizers. Here the degenerate expression Du/|Du| has to be replaced by a suitable vector field [Formula: see text] to give meaning to the highly singular 1-Laplace operator. For minimizers of a large class of problems containing the eigenvalue problem, we obtain the surprising and remarkable fact that in general infinitely many Euler–Lagrange equations have to be satisfied.

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35

Molchanova, Evgeniya A. "Variational simulation of the spectral problem." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 75 (2022): 33–37. http://dx.doi.org/10.17223/19988621/75/3.

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The ordinary fourth-order differential equation which is the zero approximation of the eigenvalue boundary problem is solved by the variational method to produce approximate formulas for eigenvalues. To obtain an explicit formula for eigenvalues, a transition is made from the differential problem to the variational problem in the Galerkin form. Calculating integrals in it gives a general formula for eigenvalues. The selection of functions satisfying certain boundary conditions yields approximate formulas suitable for the analysis of multiparameter dependencies. In particular, it is shown how the lowest eigenvalues are determined. AMS Mathematical Subject Classification: 41A60

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36

Thanh, Dang Ngoc Hoang. "A variational approach to denoising problem." ELCVIA Electronic Letters on Computer Vision and Image Analysis 15, no. 2 (November 4, 2016): 19. http://dx.doi.org/10.5565/rev/elcvia.991.

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37

Maulbetsch, Christian, and Sergei V. Shabanov. "The inverse variational problem for autoparallels." Journal of Physics A: Mathematical and General 32, no. 28 (January 1, 1999): 5355–66. http://dx.doi.org/10.1088/0305-4470/32/28/313.

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38

Arendt, Wolfgang, and Daniel Daners. "The Dirichlet problem by variational methods." Bulletin of the London Mathematical Society 40, no. 1 (February 2008): 51–56. http://dx.doi.org/10.1112/blms/bdm091.

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39

Bloch, Anthony M., Peter E. Crouch, and Amit K. Sanyal. "A variational problem on Stiefel manifolds." Nonlinearity 19, no. 10 (August 25, 2006): 2247–76. http://dx.doi.org/10.1088/0951-7715/19/10/002.

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40

Tavakoli, M., A. P. Farajzadeh, and D. Inoan. "On a generalized variational inequality problem." Filomat 32, no. 7 (2018): 2433–41. http://dx.doi.org/10.2298/fil1807433t.

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In this paper, a sufficient condition in order to have C-udomonotone property for multifunctions is presented. By applying a special minimax theorem and KKM theory some existence results of solutions of a generalized variational inequality problem are established. Some examples in order to illustrate the main results are given. The results of this paper can be considered as extension and improvement of some articles in this area.

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41

Lai, Hang-Chin, Jin-Chirng Lee, and Shuh-Jye Chern. "A variational problem and optimal control." Journal of Industrial & Management Optimization 7, no. 4 (2011): 967–75. http://dx.doi.org/10.3934/jimo.2011.7.967.

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42

Sogo, Kiyoshi. "Variational Discretization of Euler's Elastica Problem." Journal of the Physical Society of Japan 75, no. 6 (June 15, 2006): 064007. http://dx.doi.org/10.1143/jpsj.75.064007.

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43

Amar, Micòl, and Carlo Mariconda. "A Nonconvex Variational Problem with Constraints." SIAM Journal on Control and Optimization 33, no. 1 (January 1995): 299–307. http://dx.doi.org/10.1137/s0363012992235043.

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44

Aranda, E., and P. Pedregal. "A variational problem in electricity markets." Nonlinear Analysis: Real World Applications 11, no. 3 (June 2010): 2044–55. http://dx.doi.org/10.1016/j.nonrwa.2009.05.007.

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45

Saha, A., and B. Talukdar. "Inverse Variational Problem for Nonstandard Lagrangians." Reports on Mathematical Physics 73, no. 3 (June 2014): 299–309. http://dx.doi.org/10.1016/s0034-4877(14)60046-x.

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46

Casas, M., S. Martı́nez, F. Pennini, and A. Plastino. "Thermodynamics and the Tsallis variational problem." Physica A: Statistical Mechanics and its Applications 305, no. 1-2 (March 2002): 41–47. http://dx.doi.org/10.1016/s0378-4371(01)00637-9.

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47

Luc, D. T. "An Abstract Problem in Variational Analysis." Journal of Optimization Theory and Applications 138, no. 1 (April 22, 2008): 65–76. http://dx.doi.org/10.1007/s10957-008-9371-9.

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48

Khavinson, Dmitry, Mihai Putinar, and Harold S. Shapiro. "Poincaré’s Variational Problem in Potential Theory." Archive for Rational Mechanics and Analysis 185, no. 1 (October 18, 2006): 143–84. http://dx.doi.org/10.1007/s00205-006-0045-1.

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49

Shen, Xiaohua, and Wanghui Yu. "A variational problem with impurity set." Journal of Differential Equations 244, no. 11 (June 2008): 2836–69. http://dx.doi.org/10.1016/j.jde.2008.01.026.

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50

Scarpini, F. "A nonlinear variational Neumann's type problem." Calcolo 24, no. 1 (March 1987): 23–44. http://dx.doi.org/10.1007/bf02576414.

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