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On Gap Functions for Quasi-Variational Inequalities [PDF]
Abstract and Applied Analysis, 2008 For variational inequalities, various merit functions, such as the gap function, the regularized gap function, the D-gap function and so on, have been proposed.
Kouichi Taji
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Expected Residual Minimization Method for a Class of Stochastic Quasivariational Inequality Problems [PDF]
Journal of Applied Mathematics, 2012 We consider the expected residual minimization method for a class of stochastic quasivariational inequality problems (SQVIP). The regularized gap function for quasivariational inequality problem (QVIP) is in general not differentiable. We first show that
Hui-Qiang Ma, Nan-Jing Huang
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On Penalty and Gap Function Methods for Bilevel Equilibrium Problems [PDF]
Journal of Applied Mathematics, 2011 We consider bilevel pseudomonotone equilibrium problems. We use a penalty function to convert a bilevel problem into one-level ones. We generalize a pseudo-∇-monotonicity concept from ∇-monotonicity and prove that under pseudo-∇-monotonicity property any
Bui Van Dinh, Le Dung Muu
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Weighted Method for Uncertain Nonlinear Variational Inequality Problems [PDF]
Mathematics, 2019 A convex combined expectations regularized gap function with uncertain variable is presented to deal with uncertain nonlinear variational inequality problems (UNVIP).
Cunlin Li, Mihai Postolache, Zhifu Jia
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Convergence Analysis of the Approximation Problems for Solving Stochastic Vector Variational Inequality Problems [PDF]
Complexity, 2020 In this paper, we consider stochastic vector variational inequality problems (SVVIPs). Because of the existence of stochastic variable, the SVVIP may have no solutions generally.
Meiju Luo, Kun Zhang
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BMC Bioinformatics, 2023 Background Deep generative models naturally become nonlinear dimension reduction tools to visualize large-scale datasets such as single-cell RNA sequencing datasets for revealing latent grouping patterns or identifying outliers.
Gwangwoo Kim, Hyonho Chun
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Gap functions and error bounds for vector inverse mixed quasi-variational inequality problems
Fixed Point Theory and Applications, 2019 This paper is devoted to investigating a vector inverse mixed quasi-variational inequality (VIMQVI). Our aim is to obtain error bounds for VIMQVI in terms of different gap functions, i.e., the residual gap function, the regularized gap function, and the ...
Zhong-bao Wang, Zhang-you Chen, Zhe Chen
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Gap functions and error bounds for random generalized variational inequality problems
Journal of Inequalities and Applications, 2016 This paper is devoted to the study of gap functions of random generalized variational inequality problems in a fuzzy environment. Further by using the residual vector we compute error bounds for random generalized variational inequality problems and we ...
Suhel Ahmad Khan +2 more
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Differentiability of regularized gap functions for a kind of variational inclusions and local uniqueness of solutions [PDF]
SCIENTIA SINICA Mathematica, 2020 Summary: In this paper, we mainly explore continuity and differentiability properties of regularized gap functions for a kind of nonconvex variational inclusions and its associated solution mapping by making use of the properties of the Moreau envelope functions of the prox-regular function and its proximal mapping.
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Optimization, 2023 The aim of this paper is to establish new results on a class of generalized mixed quasi-variational-hemivariational inequalities (GMQVHVI, for short) via regularized gap ...
Van Hung, Nguyen +3 more
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