Zeitschriftenartikel: „Armijo“

1

Lannes, Delphine. „Roberto Armijo“. Caravelle 70, Nr. 1 (1998): 269–76. http://dx.doi.org/10.3406/carav.1998.2792.

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2

Cortés, Carlos. „Adiós al poeta Armijo“. Caravelle 68, Nr. 1 (1997): 155–56. http://dx.doi.org/10.3406/carav.1997.2742.

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3

Sun, Min, und Jing Liu. „On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method“. Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/283215.

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Recently, Zhang et al. proposed a sufficient descent Polak-Ribière-Polyak (SDPRP) conjugate gradient method for large-scale unconstrained optimization problems and proved its global convergence in the sense thatlim infk→∞∥∇f(xk)∥=0when an Armijo-type line search is used. In this paper, motivated by the line searches proposed by Shi et al. and Zhang et al., we propose two new Armijo-type line searches and show that the SDPRP method has strong convergence in the sense thatlimk→∞∥∇f(xk)∥=0under the two new line searches. Numerical results are reported to show the efficiency of the SDPRP with the new Armijo-type line searches in practical computation.

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4

Pailler, Claire. „Roberto Armijo, poeta de los exilios“. Caravelle 88, Nr. 1 (2007): 267–80. http://dx.doi.org/10.3406/carav.2007.3149.

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5

Liu, Jiankun, und Shouqiang Du. „Modified Three-Term Conjugate Gradient Method and Its Applications“. Mathematical Problems in Engineering 2019 (17.04.2019): 1–9. http://dx.doi.org/10.1155/2019/5976595.

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We propose a modified three-term conjugate gradient method with the Armijo line search for solving unconstrained optimization problems. The proposed method possesses the sufficient descent property. Under mild assumptions, the global convergence property of the proposed method with the Armijo line search is proved. Due to simplicity, low storage, and nice convergence properties, the proposed method is used to solve M-tensor systems and a kind of nonsmooth optimization problems with l1-norm. Finally, the given numerical experiments show the efficiency of the proposed method.

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6

Gabison, Sharon. „Clinician's Commentary on Armijo-Olivo et al.“ Physiotherapy Canada 65, Nr. 3 (Juli 2013): 300–301. http://dx.doi.org/10.3138/ptc.2012-30bc-cc.

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7

Qi, Hou-Duo, und Xiao-Qi Yang. „Armijo Newton method for convex best interpolation“. Optimization Methods and Software 21, Nr. 2 (April 2006): 179–200. http://dx.doi.org/10.1080/10556780500065432.

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8

Si, Binghui, Zhichao Tian, Wenqiang Chen, Xing Jin, Xin Zhou und Xing Shi. „Performance Assessment of Algorithms for Building Energy Optimization Problems with Different Properties“. Sustainability 11, Nr. 1 (20.12.2018): 18. http://dx.doi.org/10.3390/su11010018.

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Assessing the performance of algorithms in solving building energy optimization (BEO) problems with different properties is essential for selecting appropriate algorithms to achieve the best design solution. This study begins with a classification of the properties of BEO problems from three perspectives, namely, design variables, objective functions, and constraints. An analytical approach and a numerical approach are proposed to determine the properties of BEO problems. Six BEO test problems with different properties, namely, continuous vs. discrete, convex vs. non-convex, linear vs. non-linear, uni-modal vs. multimodal, and single-dimensional vs. multi-dimensional, are composed to evaluate the performance of algorithms. The selected optimization algorithms for performance assessment include the discrete Armijo gradient, Particle Swarm Optimization (PSO), Hooke-Jeeves, and hybrid PSO and Hooke-Jeeves. The assessment results indicate that multimodality can cause Hooke-Jeeves and discrete Armijo gradient algorithms to fall into local optima traps. The convex, non-convex, linear and non-linear properties of uni-modal BEO problems have little impact on the performance behavior of the algorithms. The discrete Armijo gradient and Hooke-Jeeves are not recommended for solving discrete and multi-dimensional BEO problems.

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9

Castro Zúñiga, Amanda Lizet. „Esta Patria, Este Amor... de Oscar Amaya-Armijo“. Revista Iberoamericana 57, Nr. 154 (03.03.1991): 389–91. http://dx.doi.org/10.5195/reviberoamer.1991.4892.

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10

Shi, Zhenjun, und Shengquan Wang. „Modified nonmonotone Armijo line search for descent method“. Numerical Algorithms 57, Nr. 1 (03.07.2010): 1–25. http://dx.doi.org/10.1007/s11075-010-9408-7.

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11

Dai, Yu-Hong. „Conjugate Gradient Methods with Armijo-type Line Searches“. Acta Mathematicae Applicatae Sinica, English Series 18, Nr. 1 (März 2002): 123–30. http://dx.doi.org/10.1007/s102550200010.

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12

Velez, German Correa, Fernando Mesa und Pedro Pablo Cardenas Alzate. „Linear search optimization through the Armijo rule method“. Contemporary Engineering Sciences 11, Nr. 16 (2018): 771–78. http://dx.doi.org/10.12988/ces.2018.8121.

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13

Ahookhosh, Masoud, und Susan Ghaderi. „On efficiency of nonmonotone Armijo-type line searches“. Applied Mathematical Modelling 43 (März 2017): 170–90. http://dx.doi.org/10.1016/j.apm.2016.10.055.

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14

Espinosa Aguirre, Joaquin Edgardo. „Sobre Eduardo Miranda Arrieta y José Magaña Morales, Por el rey y por la independencia mexicana. José Gabriel Armijo y Vicente Guerrero (1814-1821)“. Estudios de Historia Moderna y Contemporánea de México, Nr. 63 (31.03.2022): 251–56. http://dx.doi.org/10.22201/iih.24485004e.2022.63.77701.

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Reseña sobre Eduardo Miranda Arrieta y José Magaña Morales. Por el rey y por la independencia mexicana. José Gabriel Armijo y Vicente Guerrero (1814-1821). Morelia: Universidad Michoacana de San Nicolás de Hidalgo, Instituto de Investigaciones Históricas, 2019.

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15

Wardi, Y. „Stochastic algorithms with armijo stepsizes for minimization of functions“. Journal of Optimization Theory and Applications 64, Nr. 2 (Februar 1990): 399–417. http://dx.doi.org/10.1007/bf00939456.

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16

Rahali, Nour E., Nacera Djeghaba und Rachid Benzine. „Global convergence of the Armijo epsilon steepest descent algorithm“. Journal of Numerical Analysis and Approximation Theory 41, Nr. 2 (01.08.2012): 169–80. http://dx.doi.org/10.33993/jnaat412-978.

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In this article, we study the unconstrained minimization problem\[(P)\,\,\,\min\left\{ f(x):x\in\mathbb{R}^{n}\right\} .\]where \(f:\mathbb{R}^{n}\rightarrow\mathbb{R}\) is a continuously differentiable function. We introduce a new algorithm which accelerates the convergence of the steepest descent method. We further establish the global convergence of this algorithm in the case of Armijo inexact line search.

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17

Magaldi, Nuria, und Antonio Bueno Armijo. „Presentación“. DOCENCIA Y DERECHO, Nr. 21 (01.06.2023): 1. http://dx.doi.org/10.21071/redd.vi21.17373.

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Presentación del número 21 de la Revista Docencia y Derecho. Monográfico coordinado por Nuria Magaldi y Antonio Bueno Armijo, Profesores Titulares de Derecho Administrativo de la Universidad de Córdoba y directores del International Colloquium on Higher Education in Foreign Languages in Law and Political Sciences.

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18

Pan, Lili, und Xunzhi Zhu. „An Armijo-Type Hard Thresholding Algorithm for Joint Sparse Recovery“. IEEE Access 9 (2021): 101765–72. http://dx.doi.org/10.1109/access.2021.3097216.

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19

Wardi, Y., M. Egerstedt und M. Hale. „Switched-mode systems: gradient-descent algorithms with Armijo step sizes“. Discrete Event Dynamic Systems 25, Nr. 4 (12.06.2014): 571–99. http://dx.doi.org/10.1007/s10626-014-0198-2.

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20

Li, Yen-Huan, und Volkan Cevher. „Convergence of the Exponentiated Gradient Method with Armijo Line Search“. Journal of Optimization Theory and Applications 181, Nr. 2 (03.12.2018): 588–607. http://dx.doi.org/10.1007/s10957-018-1428-9.

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21

Xia, Yu, Bangguo Xie, Feng Tang, Ying Ye Yu und Jinyou Li. „An improved approach of Armijo-based adaptive stability transformation method“. Structures 50 (April 2023): 1827–37. http://dx.doi.org/10.1016/j.istruc.2023.03.006.

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22

Huang, Huang und Huang. „A Novel Algorithm for Structural Reliability Analysis Based on Finite Step Length and Armijo Line Search“. Applied Sciences 9, Nr. 12 (21.06.2019): 2546. http://dx.doi.org/10.3390/app9122546.

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This paper presents a novel algorithm for structural reliability analysis based on the finite step length and Armijo line search to remove the drawbacks of the Hasofer–Lind and Rakwitz–Fiessler (HL-RF) algorithm that may be subjected to non-convergence in the first-order reliability method (FORM). Initially, the sensitivity factor with finite step length is introduced for preventing the iterative process of the algorithm from entering a periodic loop. Subsequently, an optimization method based on the sufficient descent condition with the Armijo line search technique is proposed. With that, the initial step length and adjusting coefficient are optimized to enhance the applicability of the algorithm emphatically for highly nonlinear functions. A comparison analysis is carried out between the proposed algorithm and existing FORM-based algorithms to validate the robustness and efficiency of the proposed algorithm. The results of this demonstrate that the proposed algorithm is superior to the HL-RF algorithm in terms of robustness and surpass the other existing FORM-based algorithms in connection to efficiency.

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23

Muciño Ruiz, José Antonio. „Carmen Elena Armijo Canto. Fábula y mundo: Odo de Chériton y el “Libro de los gatos”. México: UNAM-IIFL: Centro de Poética, 2014.“ Acta Poética 37, Nr. 2 (06.06.2016): 124. http://dx.doi.org/10.19130/iifl.ap.2016.2.738.

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La publicación del libro Fábula y mundo: Odo de Chériton y el “Libro de los gatos” de Carmen Elena Armijo Canto, profesora e investigadora de la Universidad Nacional Autónoma de México (UNAM), es una importante contribución a los estudios medievales hispánicos realizados en México, cuyo alcance se proyecta a todo el mundo académico interesado en la cultura medieval española.

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24

Ali Al-Hawasy, Jamil A., und Eman H. Al-Rawdanee. „Numerical Solution for Classical Optimal Control Problem Governing by Hyperbolic Partial Differential Equation via Galerkin Finite Element-Implicit method with Gradient Projection Method“. Ibn AL- Haitham Journal For Pure and Applied Science 32, Nr. 2 (20.05.2019): 71. http://dx.doi.org/10.30526/32.2.2141.

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This paper deals with the numerical solution of the discrete classical optimal control problem (DCOCP) governing by linear hyperbolic boundary value problem (LHBVP). The method which is used here consists of: the GFEIM " the Galerkin finite element method in space variable with the implicit finite difference method in time variable" to find the solution of the discrete state equation (DSE) and the solution of its corresponding discrete adjoint equation, where a discrete classical control (DCC) is given. The gradient projection method with either the Armijo method (GPARM) or with the optimal method (GPOSM) is used to solve the minimization problem which is obtained from the necessary condition for optimality of the DCOCP to find the DCC.An algorithm is given and a computer program is coded using the above methods to find the numerical solution of the DCOCP with step length of space variable , and step length of time variable . Illustration examples are given to explain the efficiency of these methods. The results show the methods which are used here are better than those obtained when we used the Gradient method (GM) or Frank Wolfe method (FWM) with Armijo step search method to solve the minimization problem.

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25

Rodríguez-Rodríguez, Luis Pablo. „Excmo. Sr. D. Manuel Armijo Valenzuela, Tercer Catedrático (1963 a 1986)“. Boletin Sociedad Española Hidrologia Medica 27, Nr. 1 (2012): 21–29. http://dx.doi.org/10.23853/bsehm.2017.0393.

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26

Keshtegar, Behrooz, Reza Kolahchi, José A. F. O. Correia, Nicholas Fantuzzi und Mohammad Hassan Mirabimoghaddam. „Reliability Analysis of Composite-Nanofluid Tube Using Finite-Based Armijo Method“. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering 7, Nr. 4 (Dezember 2021): 04021057. http://dx.doi.org/10.1061/ajrua6.0001177.

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27

陈, 咪. „A Modified Levenberg-Marquardt Method with an Armijo Nonmonotone Line Search“. Advances in Applied Mathematics 11, Nr. 09 (2022): 6511–20. http://dx.doi.org/10.12677/aam.2022.119689.

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28

Qiufeng Shang, 尚秋峰, 秦文婕 Wenjie Qin und 胡雨婷 Yuting Hu. „Brillouin Scattering Spectral Image Denoising Algorithm Based on Armijo Line Search“. Chinese Journal of Lasers 46, Nr. 9 (2019): 0906002. http://dx.doi.org/10.3788/cjl201946.0906002.

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29

Anh, P. N., und H. A. Le Thi. „An Armijo-type method for pseudomonotone equilibrium problems and its applications“. Journal of Global Optimization 57, Nr. 3 (04.09.2012): 803–20. http://dx.doi.org/10.1007/s10898-012-9970-8.

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30

Bai, Jianchao, Xuefeng Duan, Kexin Cheng und Xuewei Zhang. „A Class of Weighted Low Rank Approximation of the Positive Semidefinite Hankel Matrix“. Journal of Applied Mathematics 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/937573.

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We consider the weighted low rank approximation of the positive semidefinite Hankel matrix problem arising in signal processing. By using the Vandermonde representation, we firstly transform the problem into an unconstrained optimization problem and then use the nonlinear conjugate gradient algorithm with the Armijo line search to solve the equivalent unconstrained optimization problem. Numerical examples illustrate that the new method is feasible and effective.

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31

Jiang, Huabin, Songhai Deng, Xiaodong Zheng und Zhong Wan. „Global Convergence of a Modified Spectral Conjugate Gradient Method“. Journal of Applied Mathematics 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/641276.

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A modified spectral PRP conjugate gradient method is presented for solving unconstrained optimization problems. The constructed search direction is proved to be a sufficiently descent direction of the objective function. With an Armijo-type line search to determinate the step length, a new spectral PRP conjugate algorithm is developed. Under some mild conditions, the theory of global convergence is established. Numerical results demonstrate that this algorithm is promising, particularly, compared with the existing similar ones.

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32

Al-Bayati, Abbas, und Runak Abdullah. „New Hybrid (Oren- Al-Bayati) Self-Scaling Algorithm With Armijo Line-Search“. AL-Rafidain Journal of Computer Sciences and Mathematics 7, Nr. 2 (01.12.2010): 39–47. http://dx.doi.org/10.33899/csmj.2010.163883.

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33

Wasi, H. A., und Mushtak A. K. Shiker. „Nonlinear Conjugate Gradient Method with Modified Armijo Condition to Solve Unconstrained Optimization“. Journal of Physics: Conference Series 1818, Nr. 1 (01.03.2021): 012021. http://dx.doi.org/10.1088/1742-6596/1818/1/012021.

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34

Huang, Yuanyuan. „Numerical Behaviors of Conjugate Gradient Methods with an Armijo Type Line Search“. Journal of Information and Computational Science 11, Nr. 6 (10.04.2014): 1723–31. http://dx.doi.org/10.12733/jics20103186.

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35

Ahookhosh, Masoud, Keyvan Amini und Somayeh Bahrami. „A class of nonmonotone Armijo-type line search method for unconstrained optimization“. Optimization 61, Nr. 4 (April 2012): 387–404. http://dx.doi.org/10.1080/02331934.2011.641126.

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36

Wang, Zhujun, Li Cai und Zheng Peng. „A family of global convergent inexact secant methods for nonconvex constrained optimization“. Journal of Algorithms & Computational Technology 12, Nr. 2 (02.04.2018): 165–76. http://dx.doi.org/10.1177/1748301818762497.

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We present a family of new inexact secant methods in association with Armijo line search technique for solving nonconvex constrained optimization. Different from the existing inexact secant methods, the algorithms proposed in this paper need not compute exact directions. By adopting the nonsmooth exact penalty function as the merit function, the global convergence of the proposed algorithms is established under some reasonable conditions. Some numerical results indicate that the proposed algorithms are both feasible and effective.

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37

Zhang, Mengxiang, Yingjie Zhou und Songhua Wang. „A Modified Nonlinear Conjugate Gradient Method with the Armijo Line Search and Its Application“. Mathematical Problems in Engineering 2020 (28.08.2020): 1–14. http://dx.doi.org/10.1155/2020/6210965.

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In this article, a modified Polak-Ribière-Polyak (PRP) conjugate gradient method is proposed for image restoration. The presented method can generate sufficient descent directions without any line search conditions. Under some mild conditions, this method is globally convergent with the Armijo line search. Moreover, the linear convergence rate of the modified PRP method is established. The experimental results of unconstrained optimization, image restoration, and compressive sensing show that the proposed method is promising and competitive with other conjugate gradient methods.

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38

Dong, Wen-Li, Xing Li und Zheng Peng. „A Simulated Annealing-Based Barzilai–Borwein Gradient Method for Unconstrained Optimization Problems“. Asia-Pacific Journal of Operational Research 36, Nr. 04 (August 2019): 1950017. http://dx.doi.org/10.1142/s0217595919500179.

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In this paper, we propose a simulated annealing-based Barzilai–Borwein (SABB) gradient method for unconstrained optimization problems. The SABB method accepts the Barzilai–Borwein (BB) step by a simulated annealing rule. If the BB step cannot be accepted, the Armijo line search is used. The global convergence of the SABB method is established under some mild conditions. Numerical experiments indicate that, compared to some existing BB methods using nonmonotone line search technique, the SABB method performs well with high efficiency.

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Fossey, Richard, und Perry A. Zirkel. „Liability for Student Suicide in the Wake of Eisel“. Texas Wesleyan Law Review 10, Nr. 2 (März 2004): 403–39. http://dx.doi.org/10.37419/twlr.v10.i2.5.

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In the wake of Eisel, few commentaries have been written about the legal significance of student suicide. Although providing broad practical advice and limited case law analysis, the professional literature lacks a comprehensive and systematic analysis of Eisel's common-law and constitutional tort effects. To fill this gap and address this question in terms of common law and constitutional liability, this Article is organized as follows. Part II provides a brief overview of the common law regarding liability for another's suicide and shows that courts have generally disfavored this cause of action. Section III examines the Eisel decision in detail. Part III(A) traces the post-Eisel decisions that took the same common-law path to possible liability. Part III(B) analyzes why public educators do not need to be overly concerned with common-law liability for student suicides. Part IV examines the post-Eisel decisions that proceeded down the alternate path of an alleged constitutional tort. Part V examines the Armijo v. Wagon Mound Public School decision and demonstrates that the court established the possibility of § 1983 liability on the part of school officials in the wake of student suicide. Part V.A examines the pre- and post-Armijo cases addressing student suicide. Part V.B analyzes the unlikely probability of success under a § 1983 claim against school officials. Part VI provides a brief conclusion that educators have little to fear with regard to liability for a student's suicide.

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40

Wu, Qing. „A Novel Smooth Support Vector Regression Based on CHKS Function“. Applied Mechanics and Materials 44-47 (Dezember 2010): 3746–51. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.3746.

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This paper presents a new smooth approach to solve support vector regression (SVR). Based on Karush-Kuhn-Tucker complementary condition in optimization theory, a smooth unconstrained optimization model for SVR is built. Since the objective function of the unconstrained SVR model is non-smooth, we apply the smooth techniques and replace the ε-insensitive loss function by CHKS function. Newton-Armijo algorithm is used to solve the smooth CHKS-SSVR model. Primary numerical results illustrate that our proposed approach improves the regression performance and the learning efficiency.

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Ketabchi, Saeed, und Malihe Behboodi-Kahoo. „Smoothing Techniques and Augmented Lagrangian Method for Recourse Problem of Two-Stage Stochastic Linear Programming“. Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/735916.

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The augmented Lagrangian method can be used for solving recourse problems and obtaining their normal solution in solving two-stage stochastic linear programming problems. The augmented Lagrangian objective function of a stochastic linear problem is not twice differentiable which precludes the use of a Newton method. In this paper, we apply the smoothing techniques and a fast Newton-Armijo algorithm for solving an unconstrained smooth reformulation of this problem. Computational results and comparisons are given to show the effectiveness and speed of the algorithm.

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42

Wan, Zhong, Kok Lay Teo, XianLong Shen und ChaoMing Hu. „New BFGS method for unconstrained optimization problem based on modified Armijo line search“. Optimization 63, Nr. 2 (11.01.2012): 285–304. http://dx.doi.org/10.1080/02331934.2011.644284.

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43

严, 娇娇. „The Perturbed BFGS Method for the Unconstrained Optimization with the Armijo Line Search“. Advances in Applied Mathematics 08, Nr. 02 (2019): 250–57. http://dx.doi.org/10.12677/aam.2019.82029.

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44

Wan, Zhong, Yu Chen und XiaoDong Zheng. „Solution method of optimisation problem based on a modified Armijo-type line search“. International Journal of Computational Science and Engineering 11, Nr. 3 (2015): 322. http://dx.doi.org/10.1504/ijcse.2015.072643.

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45

Román, Nicolás. „Precarios, proletarios y ambulantes: la clase trabajadora en la narrativa de Diego Armijo“. Nueva revista del Pacífico, Nr. 80 (2024): 316–46. http://dx.doi.org/10.4067/s0719-51762024000100316.

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46

Zheng, Xiuyun, und Jiarong Shi. „A Modified Sufficient Descent Polak–Ribiére–Polyak Type Conjugate Gradient Method for Unconstrained Optimization Problems“. Algorithms 11, Nr. 9 (06.09.2018): 133. http://dx.doi.org/10.3390/a11090133.

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In this paper, a modification to the Polak–Ribiére–Polyak (PRP) nonlinear conjugate gradient method is presented. The proposed method always generates a sufficient descent direction independent of the accuracy of the line search and the convexity of the objective function. Under appropriate conditions, the modified method is proved to possess global convergence under the Wolfe or Armijo-type line search. Moreover, the proposed methodology is adopted in the Hestenes–Stiefel (HS) and Liu–Storey (LS) methods. Extensive preliminary numerical experiments are used to illustrate the efficiency of the proposed method.

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47

Lai, Kin Keung, Shashi Kant Mishra und Bhagwat Ram. „On q-Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems“. Mathematics 8, Nr. 4 (17.04.2020): 616. http://dx.doi.org/10.3390/math8040616.

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A parameter-free optimization technique is applied in Quasi-Newton’s method for solving unconstrained multiobjective optimization problems. The components of the Hessian matrix are constructed using q-derivative, which is positive definite at every iteration. The step-length is computed by an Armijo-like rule which is responsible to escape the point from local minimum to global minimum at every iteration due to q-derivative. Further, the rate of convergence is proved as a superlinear in a local neighborhood of a minimum point based on q-derivative. Finally, the numerical experiments show better performance.

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48

Collado Chaves, Adriana. „Zona de turbulencia: arte en Nicaragua, de la revolución al neoliberalismo. Raúl Quintanilla Armijo. San José: TEOR/Ética, 2018“. Anuario de Estudios Centroamericanos 45 (08.04.2019): 713–17. http://dx.doi.org/10.15517/aeca.v45i0.40713.

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Nicaragua, Arte Contemporáneo y Raúl Quintanilla Armijo. Triada indivisible caracterizada por la resistencia. Con más vidas y más garras que un gato arisco. Así al menos lo he experimentado yo. Y ahora que he concluido la lectura de este libro, confirmo que ese ser tricéfalo solo puede sobrevivir así: arañando cualquier autoridad que intente domesticarlo, saltando siempre a un abismo con el instinto de caer en cuatro patas y con la esperanza herida pero parda, para camuflarse en las largas noches en las que su patria no parece ver la luz.

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Waziri, M. Y., und Z. A. Majid. „An Enhanced Matrix-Free Secant Method via Predictor-Corrector Modified Line Search Strategies for Solving Systems of Nonlinear Equations“. International Journal of Mathematics and Mathematical Sciences 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/814587.

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Diagonal updating scheme is among the cheapest Newton-like methods for solving system of nonlinear equations. Nevertheless, the method has some shortcomings. In this paper, we proposed an improved matrix-free secant updating scheme via line search strategies, by using the steps of backtracking in the Armijo-type line search as a step length predictor and Wolfe-Like condition as corrector. Our approach aims at improving the overall performance of diagonal secant updating scheme. Under mild assumptions, the global convergence results have been presented. Numerical experiments verify that the proposed approach is very promising.

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50

Jolaoso, Lateef Olakunle, und Maggie Aphane. „An Efficient Parallel Extragradient Method for Systems of Variational Inequalities Involving Fixed Points of Demicontractive Mappings“. Symmetry 12, Nr. 11 (20.11.2020): 1915. http://dx.doi.org/10.3390/sym12111915.

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Herein, we present a new parallel extragradient method for solving systems of variational inequalities and common fixed point problems for demicontractive mappings in real Hilbert spaces. The algorithm determines the next iterate by computing a computationally inexpensive projection onto a sub-level set which is constructed using a convex combination of finite functions and an Armijo line-search procedure. A strong convergence result is proved without the need for the assumption of Lipschitz continuity on the cost operators of the variational inequalities. Finally, some numerical experiments are performed to illustrate the performance of the proposed method.

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