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Journal articles on the topic 'Variational inequalities (Mathematics)'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 January 2023

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1

Ženíšek, Alexander. "Approximations of parabolic variational inequalities." Applications of Mathematics 30, no. 1 (1985): 11–35. http://dx.doi.org/10.21136/am.1985.104124.

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2

Ding, Xie Ping, and Kok-Keong Tan. "Generalized variational inequalities and generalized quasi-variational inequalities." Journal of Mathematical Analysis and Applications 148, no. 2 (May 1990): 497–508. http://dx.doi.org/10.1016/0022-247x(90)90016-9.

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3

MACKIE, A. G. "Complementary Variational Inequalities." IMA Journal of Applied Mathematics 36, no. 3 (1986): 293–305. http://dx.doi.org/10.1093/imamat/36.3.293.

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4

Lavrenyuk, S. P., and N. P. Protsakh. "Variational Ultraparabolic Inequalities." Ukrainian Mathematical Journal 56, no. 12 (December 2004): 1915–31. http://dx.doi.org/10.1007/s11253-005-0159-x.

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5

Cong-jun, Zhang. "Generalized variational inequalities and generalized quasi-variational inequalities." Applied Mathematics and Mechanics 14, no. 4 (April 1993): 333–44. http://dx.doi.org/10.1007/bf02465170.

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6

Liu, Zhenhai. "Generalized quasi-variational hemi-variational inequalities." Applied Mathematics Letters 17, no. 6 (June 2004): 741–45. http://dx.doi.org/10.1016/s0893-9659(04)90115-2.

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7

Yu, Su-Jane, and Jen-Chih Yao. "On the Generalized Nonlinear Variational Inequalities and Quasi-Variational Inequalities." Journal of Mathematical Analysis and Applications 198, no. 1 (February 1996): 178–93. http://dx.doi.org/10.1006/jmaa.1996.0075.

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8

NOOR, MUHAMMAD ASLAM. "SOME NONLINEAR VARIATIONAL INEQUALITIES." Tamkang Journal of Mathematics 26, no. 2 (June 1, 1995): 97–105. http://dx.doi.org/10.5556/j.tkjm.26.1995.4382.

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In this paper, we introduce and study a new class of variational in- equalities. Using the auxiliary principle technique, we prove the existence of a solution of this class of variational inequalities and suggest a new and novel itera- tive algorithm. Several special cases, which can be obtained from the main results, are also discussed.

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9

Noor, Muhammad Aslam. "Mixed quasi variational inequalities." Applied Mathematics and Computation 146, no. 2-3 (December 2003): 553–78. http://dx.doi.org/10.1016/s0096-3003(02)00605-7.

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10

Noor, Muhammad Aslam. "Well-posed variational inequalities." Journal of Applied Mathematics and Computing 11, no. 1-2 (May 2003): 165–72. http://dx.doi.org/10.1007/bf02935729.

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11

Chang, S. S., and C. J. Zhang. "On a Class of Generalized Variational Inequalities and Quasi-Variational Inequalities." Journal of Mathematical Analysis and Applications 179, no. 1 (October 1993): 250–59. http://dx.doi.org/10.1006/jmaa.1993.1348.

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12

Lin, Lai-Jiu. "Pre-vector variational inequalities." Bulletin of the Australian Mathematical Society 53, no. 1 (February 1996): 63–70. http://dx.doi.org/10.1017/s0004972700016725.

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Existence theorems for pre-vector variational inequalities are established under different conditions on the operator T and the function η. As an application, we establish the existence of a weak minimum of an optimisation problem on η-invex functions.

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13

Liu, Zhen-Hai. "Elliptic variational hemivariational inequalities." Applied Mathematics Letters 16, no. 6 (August 2003): 871–76. http://dx.doi.org/10.1016/s0893-9659(03)90010-3.

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14

Soleimani-damaneh, M. "Penalization for variational inequalities." Applied Mathematics Letters 22, no. 3 (March 2009): 347–50. http://dx.doi.org/10.1016/j.aml.2008.03.029.

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15

Goeleven, D., D. Motreanu, and P. D. Panagiotopoulos. "Semicoercive variational hemivariational inequalities." Applicable Analysis 65, no. 1-2 (June 1997): 119–34. http://dx.doi.org/10.1080/00036819708840553.

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16

McLinden, L. "Stable monotone variational inequalities." Mathematical Programming 48, no. 1-3 (March 1990): 303–38. http://dx.doi.org/10.1007/bf01582261.

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17

Noor, Muhammad Aslam. "General nonlinear variational inequalities." Journal of Mathematical Analysis and Applications 126, no. 1 (August 1987): 78–84. http://dx.doi.org/10.1016/0022-247x(87)90075-8.

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18

Ganguly, Ashok, and Kamal Wadhwa. "On Random Variational Inequalities." Journal of Mathematical Analysis and Applications 206, no. 1 (February 1997): 315–21. http://dx.doi.org/10.1006/jmaa.1997.5194.

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19

Peng, Jianwen. "System of generalised set-valued quasi-variational-like inequalities." Bulletin of the Australian Mathematical Society 68, no. 3 (December 2003): 501–15. http://dx.doi.org/10.1017/s0004972700037904.

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In this paper, we shall introduce a system of generalised set-valued quasi-variational-like inequalities, which generalises and unifies systems of generalised vector variational inequalities, systems of variational inequalities, generalised vector quasi-variational-like inequalities as well as various extensions of the classic variational inequalities in the literature. Some existence results for a solution of a system of generalized set-valued quasi-variational-like inequalities without any monotonity are obtained.

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20

Noor, Muhammad Aslam. "Pseudomonotone general mixed variational inequalities." Applied Mathematics and Computation 141, no. 2-3 (September 2003): 529–40. http://dx.doi.org/10.1016/s0096-3003(02)00273-4.

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21

Noor, Muhammad Aslam. "Mixed quasi regularized variational inequalities." Mathematical Inequalities & Applications, no. 4 (2006): 761–69. http://dx.doi.org/10.7153/mia-09-67.

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22

Jacimovic, Milojica, and Izedin Krnic. "A posteriori bounds of approximate solution to variational and quasi-variational inequalities." Filomat 25, no. 1 (2011): 163–71. http://dx.doi.org/10.2298/fil1101163j.

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In this paper we present some bounds of an approximate solution to variational and quasi-variational inequalities. The measures of errors can be used for construction of iterative and continuous procedures for solving variational (quasi-variational) inequalities and formulation of corresponding stopping rules. We will also present some methods based on linearization for solving quasi-variational inequalities.

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23

Ansari, Q. H., Z. Khan, and A. H. Siddiqi. "Weighted Variational Inequalities." Journal of Optimization Theory and Applications 127, no. 2 (November 2005): 263–83. http://dx.doi.org/10.1007/s10957-005-6539-4.

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24

Panagiotopoulos, Panagiotis D. "Variational-hemivariational inequalities in nonlinear elasticity. The coercive case." Applications of Mathematics 33, no. 4 (1988): 249–68. http://dx.doi.org/10.21136/am.1988.104307.

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25

Gwinner, J. "Discretization of semicoercive variational inequalities." Aequationes Mathematicae 42, no. 1 (August 1991): 72–79. http://dx.doi.org/10.1007/bf01818479.

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26

Batool, Safeera, Muhammad Aslam Noor, and Khalida Inayat Noor. "Merit functions for absolute value variational inequalities." AIMS Mathematics 6, no. 11 (2021): 12133–47. http://dx.doi.org/10.3934/math.2021704.

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<abstract><p>This article deals with a class of variational inequalities known as absolute value variational inequalities. Some new merit functions for the absolute value variational inequalities are established. Using these merit functions, we derive the error bounds for absolute value variational inequalities. Since absolute value variational inequalities contain variational inequalities, absolute value complementarity problem and system of absolute value equations as special cases, the findings presented here recapture various known results in the related domains. The conclusions of this paper are more comprehensive and may provoke futuristic research.</p></abstract>

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27

Klimov, V. S., and N. A. Dem’yankov. "Relative rotation and variational inequalities." Russian Mathematics 55, no. 6 (May 25, 2011): 37–45. http://dx.doi.org/10.3103/s1066369x11060065.

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28

Liu, Honghai, and Hanbin Wang. "VARIATIONAL INEQUALITIES FOR BILINEAR AVERAGES." Mathematika 66, no. 3 (May 4, 2020): 622–39. http://dx.doi.org/10.1112/mtk.12034.

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29

Chebotarev, A. Yu, and A. S. Savenkova. "Variational inequalities in magneto-hydrodynamics." Mathematical Notes 82, no. 1-2 (July 2007): 119–30. http://dx.doi.org/10.1134/s0001434607070152.

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30

Peng, Jian-Wen, Nan-Jing Huang, Xue-Xiang Huang, and Jen-Chih Yao. "Variational Inequalities and Vector Optimization." Journal of Applied Mathematics 2013 (2013): 1. http://dx.doi.org/10.1155/2013/245485.

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31

Park, Jong Yeoul, and Jae Ug Jeong. "Parametric generalized mixed variational inequalities." Applied Mathematics Letters 17, no. 1 (January 2004): 43–48. http://dx.doi.org/10.1016/s0893-9659(04)90009-2.

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32

Aslam Noor, Muhammad, Khalida Inayat Noor, and Huma Yaqoob. "On General Mixed Variational Inequalities." Acta Applicandae Mathematicae 110, no. 1 (December 17, 2008): 227–46. http://dx.doi.org/10.1007/s10440-008-9402-4.

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33

Butt, Rizwan. "Penalty Method for Variational Inequalities." Advances in Applied Mathematics 18, no. 4 (May 1997): 423–31. http://dx.doi.org/10.1006/aama.1996.0521.

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34

Plum, M., and Ch Wieners. "Numerical Enclosures for Variational Inequalities." Computational Methods in Applied Mathematics 7, no. 4 (2007): 376–88. http://dx.doi.org/10.2478/cmam-2007-0023.

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AbstractWe present a new method for proving the existence of a unique solution of variational inequalities within guaranteed close error bounds to a numerical approximation. The method is derived for a specific model problem featuring most of the difficulties of perfect plasticity. We introduce a finite element method for the computation of admissible primal and dual solutions which a posteriori guarantees the existence of a unique solution (by the verification of the safe load condition) and which allows determination of a guaranteed error bound. Finally, we present explicit existence results and error bounds in some significant specific configurations.

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35

Georgiev, Pando Gr. "Parameterized variational inequalities." Journal of Global Optimization 47, no. 3 (June 24, 2009): 457–62. http://dx.doi.org/10.1007/s10898-009-9424-0.

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36

Husain, Shamshad, and Sanjeev Gupta. "Existence of solutions for generalized nonlinear vector quasi-variational-like inequalities with set-valued mappings." Filomat 26, no. 5 (2012): 909–16. http://dx.doi.org/10.2298/fil1205909h.

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In this paper, we introduce and study a class of generalized nonlinear vector quasi-variational- like inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalized mixed quasi-variational-like inequalities and so on. By means of fixed point theorem, we obtain existence theorem of solutions to the class of generalized nonlinear vector quasi-variational-like inequalities in the setting of locally convex topological vector spaces.

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37

Yao, J. C., and J. S. Guo. "Variational and Generalized Variational Inequalities with Discontinuous Mappings." Journal of Mathematical Analysis and Applications 182, no. 2 (March 1994): 371–92. http://dx.doi.org/10.1006/jmaa.1994.1092.

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38

Robinson, Stephen M. "Reduction of affine variational inequalities." Computational Optimization and Applications 65, no. 2 (October 3, 2015): 493–509. http://dx.doi.org/10.1007/s10589-015-9796-7.

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39

Crespi, Giovanni P., and Giorgio Giorgi. "Sensitivity analysis for variational inequalities." Journal of Interdisciplinary Mathematics 5, no. 2 (January 2002): 165–76. http://dx.doi.org/10.1080/09720502.2002.10700313.

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40

Németh, S. Z. "Variational inequalities on Hadamard manifolds." Nonlinear Analysis: Theory, Methods & Applications 52, no. 5 (February 2003): 1491–98. http://dx.doi.org/10.1016/s0362-546x(02)00266-3.

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41

Bogdan, M., and J. Kolumbán. "On nonlinear parametric variational inequalities." Nonlinear Analysis: Theory, Methods & Applications 67, no. 7 (October 2007): 2272–82. http://dx.doi.org/10.1016/j.na.2006.08.035.

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42

Siddiqi, A. H., and Q. H. Ansari. "General strongly nonlinear variational inequalities." Journal of Mathematical Analysis and Applications 166, no. 2 (May 1992): 386–92. http://dx.doi.org/10.1016/0022-247x(92)90305-w.

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43

Daniilidis, Aris, and Nicolas Hadjisavvas. "Coercivity conditions and variational inequalities." Mathematical Programming 86, no. 2 (November 1, 1999): 433–38. http://dx.doi.org/10.1007/s101070050097.

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44

Lawphongpanich, Siriphong, and D. W. Hearn. "Benders decomposition for variational inequalities." Mathematical Programming 48, no. 1-3 (March 1990): 231–47. http://dx.doi.org/10.1007/bf01582257.

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45

Kyparisis, Jerzy. "Solution differentiability for variational inequalities." Mathematical Programming 48, no. 1-3 (March 1990): 285–301. http://dx.doi.org/10.1007/bf01582260.

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46

Domokos, András. "Solution Sensitivity of Variational Inequalities." Journal of Mathematical Analysis and Applications 230, no. 2 (February 1999): 382–89. http://dx.doi.org/10.1006/jmaa.1998.6193.

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47

Shih, Mau-Hsiang, and Kok-Keong Tan. "Generalized bi-quasi-variational inequalities." Journal of Mathematical Analysis and Applications 143, no. 1 (October 1989): 66–85. http://dx.doi.org/10.1016/0022-247x(89)90029-2.

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48

Eldessouky, A. T. "Strongly Nonlinear Parabolic Variational Inequalities." Journal of Mathematical Analysis and Applications 181, no. 2 (January 1994): 498–504. http://dx.doi.org/10.1006/jmaa.1994.1039.

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49

Noor, Muhammad Aslam, Khalida Inayat Noor, and Michael Th Rassias. "New Trends in General Variational Inequalities." Acta Applicandae Mathematicae 170, no. 1 (October 6, 2020): 981–1064. http://dx.doi.org/10.1007/s10440-020-00366-2.

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Abstract It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of unrelated problems, which arise in pure and applied sciences. In this paper, we present a number of new and known numerical techniques for solving general variational inequalities and equilibrium problems using various techniques including projection, Wiener-Hopf equations, dynamical systems, the auxiliary principle and the penalty function. General variational-like inequalities are introduced and investigated. Properties of higher order strongly general convex functions have been discussed. The auxiliary principle technique is used to suggest and analyze some iterative methods for solving higher order general variational inequalities. Some new classes of strongly exponentially general convex functions are introduced and discussed. Our proofs of convergence are very simple as compared with other methods. Our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems. Since the general variational inequalities include (quasi) variational inequalities and (quasi) implicit complementarity problems as special cases, these results continue to hold for these problems. Some numerical results are included to illustrate the efficiency of the proposed methods. Several open problems have been suggested for further research in these areas.

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50

Rouhani, B. Djafari, and A. A. Khan. "On the embedding of variational inequalities." Proceedings of the American Mathematical Society 131, no. 12 (December 1, 2003): 3861–71. http://dx.doi.org/10.1090/s0002-9939-03-07000-x.

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