• Title/Summary/Keyword: inequality problems

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GENERAL NONCONVEX SPLIT VARIATIONAL INEQUALITY PROBLEMS

  • Kim, Jong Kyu;Salahuddin, Salahuddin;Lim, Won Hee
    • Korean Journal of Mathematics
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    • v.25 no.4
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    • pp.469-481
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    • 2017
  • In this paper, we established a general nonconvex split variational inequality problem, this is, an extension of general convex split variational inequality problems in two different Hilbert spaces. By using the concepts of prox-regularity, we proved the convergence of the iterative schemes for the general nonconvex split variational inequality problems. Further, we also discussed the iterative method for the general convex split variational inequality problems.

APPROXIMATE PROJECTION ALGORITHMS FOR SOLVING EQUILIBRIUM AND MULTIVALUED VARIATIONAL INEQUALITY PROBLEMS IN HILBERT SPACE

  • Khoa, Nguyen Minh;Thang, Tran Van
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.4
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    • pp.1019-1044
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    • 2022
  • In this paper, we propose new algorithms for solving equilibrium and multivalued variational inequality problems in a real Hilbert space. The first algorithm for equilibrium problems uses only one approximate projection at each iteration to generate an iteration sequence converging strongly to a solution of the problem underlining the bifunction is pseudomonotone. On the basis of the proposed algorithm for the equilibrium problems, we introduce a new algorithm for solving multivalued variational inequality problems. Some fundamental experiments are given to illustrate our algorithms as well as to compare them with other algorithms.

ERROR BOUNDS FOR NONLINEAR MIXED VARIATIONAL-HEMIVARIATIONAL INEQUALITY PROBLEMS

  • A. A. H. Ahmadini;Salahuddin;J. K. Kim
    • Nonlinear Functional Analysis and Applications
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    • v.29 no.1
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    • pp.15-33
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    • 2024
  • In this article, we considered a class of nonlinear variational hemivariational inequality problems and investigated a gap function and regularized gap function for the problems. We discussed the global error bounds for such inequalities in terms of gap function and regularized gap functions by utilizing the Clarke generalized gradient, relaxed monotonicity, and relaxed Lipschitz continuous mappings. Finally, as applications, we addressed an application to non-stationary non-smooth semi-permeability problems.

A Nonlinear Programming Approach to Biaffine Matrix Inequality Problems in Multiobjective and Structured Controls

  • Lee, Joon-Hwa;Lee, Kwan-Ho;Kwon, Wook-Hyun
    • International Journal of Control, Automation, and Systems
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    • v.1 no.3
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    • pp.271-281
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    • 2003
  • In this paper, a new nonlinear programming approach is suggested to solve biaffine matrix inequality (BMI) problems in multiobjective and structured controls. It is shown that these BMI problems are reduced to nonlinear minimization problems. An algorithm that is easily implemented with existing convex optimization codes is presented for the nonlinear minimization problem. The efficiency of the proposed algorithm is illustrated by numerical examples.

STUDY OF SOME GENERALIZED h-VARIATIONAL INEQUALITY PROBLEMS IN H-PSEUDOSPACE

  • Das, Prasanta K.;Mishra, Satya N.;Samal, Sapan K.
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.3
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    • pp.475-496
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    • 2021
  • The main aim is to define a new class of generalized h-variational inequality problems and its generalized h-variational inequality problems. We define the class of h-𝜂-invex set, h-𝜂-invex function and H-pseudospace. Existence of the solution of the problems are established in H-pseudospace with the help of H-KKM mapping theorem and HC*-condition of 𝜂 associated with the function h.

GENERALIZED VECTOR MINTY'S LEMMA

  • Lee, Byung-Soo
    • The Pure and Applied Mathematics
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    • v.19 no.3
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    • pp.281-288
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    • 2012
  • In this paper, the author defines a new generalized ${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mapping and considers the equivalence of Stampacchia-type vector variational-like inequality problems and Minty-type vector variational-like inequality problems for generalized (${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mappings in Banach spaces, called the generalized vector Minty's lemma.