Results 21 to 30 of about 4,400,793 (233)
Existence of Solutions for η-Generalized Vector Variational-Like Inequalities
Journal of Inequalities and Applications, 2010 We introduce and study a class of η-generalized vector variational-like inequalities and a class of η-generalized strong vector variational-like inequalities in the setting of Hausdorff topological vector spaces.
Xi Li, Jong Kyu Kim, Nan-Jing Huang
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On the Generalized Nonlinear Variational Inequalities and Quasi-Variational Inequalities
Journal of Mathematical Analysis and Applications, 1996 AbstractThe purpose of this paper is to investigate the existence of solutions for a class of generalized nonlinear inequalities (GNVI) and generalized nonlinear quasi-variational inequalities (GNQVI) with non-monotone set-valued operators defined on non-compact sets in locally convex Hausdorff topological vector spaces.
Su-Jane Yu, Jen-Chih Yao
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Iterative Schemes for a Class of Mixed Trifunction Variational Inequalities
Journal of Applied Mathematics, 2012 We use the auxiliary principle technique to suggest and analyze some iterative methods for solving a new class of variational inequalities, which is called the mixed trifunction variational inequality.
Muhammad Aslam Noor +2 more
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Deep Neural Network Structures Solving Variational Inequalities [PDF]
Set-Valued and Variational Analysis, 2018 Motivated by structures that appear in deep neural networks, we investigate nonlinear composite models alternating proximity and affine operators defined on different spaces. We first show that a wide range of activation operators used in neural networks
P. Combettes, J. Pesquet
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Generalized variational inequalities and generalized quasi-variational inequalities
Journal of Mathematical Analysis and Applications, 1990 AbstractA very general minimax inequality is first established. Three generalized variational inequalities are then derived, which improve those obtained by Tan and Browder. By applying a fixed point theorem of Himmelberg, two generalized quasi-variational inequalities are also proved, one of which generalizes those of Shih-Tan to the non-compact case ...
Xie Ping Ding, Kok-Keong Tan
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Parametric Extended General Mixed Variational Inequalities
Journal of Applied Mathematics, 2012 It is well known that the resolvent equations are equivalent to the extended general mixed variational inequalities. We use this alternative equivalent formulation to study the sensitivity of the extended general mixed variational inequalities without ...
Muhammad Aslam Noor
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Extragradient Method with Variance Reduction for Stochastic Variational Inequalities [PDF]
SIAM Journal on Optimization, 2017 We propose an extragradient method with stepsizes bounded away from zero for stochastic variational inequalities requiring only pseudomonotonicity.
A. Iusem +3 more
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On the solution of monotone nested variational inequalities [PDF]
arXiv, 2021 We study nested variational inequalities, which are variational inequalities whose feasible set is the solution set of another variational inequality. We present a projected averaging Tikhonov algorithm requiring the weakest conditions in the literature to guarantee the convergence to solutions of the nested variational inequality.
arxiv
A variational proof of Nash’s inequality [PDF]
Rendiconti Lincei, Matematica e Applicazioni, 2020 This paper is intended to give a characterization of the optimality case in Nash’s inequality, based on methods of nonlinear analysis for elliptic equations and techniques of the calculus of variations. By embedding the problem into a family of Gagliardo–Nirenberg inequalities, this approach reveals why optimal functions have compact support and also ...
Bouin, Emeric +2 more
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Vector Optimization Problems and Generalized Vector Variational-Like Inequalities [PDF]
Sahand Communications in Mathematical Analysis, 2020 In this paper, some properties of pseudoinvex functions, defined by means of limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality, the Stampacchia vector variational-like inequality, and the weak ...
Ildar Sadeqi, Somayeh Nadi
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