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Optimization problems with an infinite number of constraints have recently been studied in many recent literatures. This paper deals with the optimality conditions for minimax optimization problems with an infinite number of constraints (MMOP) under the fulfilment of limiting constraint qualification.
Zhong, Li-nan, Jin, Yuan-feng
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Necessary optimality conditions for minimax programming problems with mathematical constraints
Optimization, 2017In this paper, necessary optimality conditions in terms of upper and/or lower subdifferentials of both cost and constraint functions are derived for minimax optimization problems with inequality, equality and geometric constraints in the setting of non-differentiatiable and non-Lipschitz functions in Asplund spaces.
Truong, Bao Q, Khahn, P., Gupta, P.
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Optimality Conditions for Nondifferentiable Minimax Programs and Vector Optimization Problems
Journal of Optimization Theory and ApplicationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Duong Thi Kim Huyen +2 more
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Optimality Conditions at Infinity for Nonsmooth Minimax Programming Problems with Some Applications
Journal of Optimization Theory and ApplicationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nguyen Van Tuyen +2 more
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Some Optimality Conditions for Minimax Problem
Pacific Journal of OptimizationSummary: Minimax problem has an important role in optimization, global optimization, game theory, and operations research. In [\textit{R. Enkhbat} and \textit{J. Enkhbayar}, Optim. Lett. 13, No. 3, 475--483 (2019; Zbl 1423.90273)], optimality conditions have been formulated for the maxmin problem.
Enkhbat, R., Battur, G.
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Second-Order Optimality Conditions in Minimax Optimization Problems
Journal of Optimization Theory and Applications, 2012A finite-dimensional minimax problem \(\min_{x} \sup_{y\in Y} f(x,y)\) s.t. \(g(x)\in D\), \(h(x)=0\) with \(x\in \mathbb R^n\), \(Y\subset \mathbb R^m\) compact, \(D\subset \mathbb R^m\) closed with nonempty interior, \(f(\cdot,y),y\in Y\); \(g\); \(h\) \(C(1,1)\) functions is reformulated and dealt with cone constraint as infinite programming problem
Anulekha Dhara, Aparna Mehra
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Approximate optimality conditions for minimax programming problems
Optimization, 2009In this article we study non-smooth Lipschitz programming problems with set inclusion and abstract constraints. Our aim is to develop approximate optimality conditions for minimax programming problems in absence of any constraint qualification. The optimality conditions are worked out not exactly at the optimal solution but at some points in a ...
Anulekha Dhara, Aparna Mehra
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