Browsing by Author "K.K. Lai"

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3rd International Joint Conference on Computational Sciences and Optimization, CSO 2010: Theoretical Development and Engineering Practice: Message from general co-chairs and program co-chairs
(2010) K.K. Lai; Yingwen Song; Shouyang Wang; W.K. Ching; Hai Jin; Jianping Li; S.K. Mishra; Lean Yu
[No abstract available]
Duality results for interval-valued semiinfinite optimization problems with equilibrium constraints using convexificators
(Institute for Ionics, 2022) K.K. Lai; S.K. Mishra; Mohd Hassan; Jaya Bisht; J.K. Maurya
This paper deals with the study of interval-valued semiinfinite optimization problems with equilibrium constraints (ISOPEC) using convexificators. First, we formulate Wolfe-type dual problem for (ISOPEC) and establish duality results between the (ISOPEC) and the corresponding Wolfe-type dual under the assumption of ∂∗-convexity. Second, we formulate Mond–Weir-type dual problem and propose duality results between the (ISOPEC) and the corresponding Mond–Weir-type dual under the assumption of ∂∗-convexity, ∂∗-pseudoconvexity, and ∂∗-quasiconvexity. © 2022, The Author(s).
Gap function for set-valued vector variational-like inequalities
(Springer New York, 2008) S.K. Mishra; S.Y. Wang; K.K. Lai
Variational-like inequalities with set-valued mappings are very useful in economics and nonsmooth optimization problems. In this paper, we study the existence of solutions and the formulation of solution methods for vector variational-like inequalities (VVLI) with set-valued mappings. We introduce gap functions and establish necessary and sufficient conditions for the existence of a solution of the VVLI. We investigate the existence of a solution for the generalized VVLI with a set-valued mapping by exploiting the existence of a solution of the VVLI with a single-valued function and a continuous selection theorem. © 2008 Springer Science+Business Media, LLC.
On characterization of solution sets of nonsmooth pseudoinvex minimization problems
(2009) S.K. Mishra; K.K. Lai
We establish some characterizations of the solution set of nonsmooth pseudoinvex minimization problems where the function involved is locally Lipschitz and Clarke differentiable. Our results extend and unify several results from the literature to nonsmooth case. © 2009 IEEE.
Optimality and duality for minimax fractional programming with support function under (C, α, ρ, d) -convexity
(Elsevier, 2015) S.K. Mishra; K.K. Lai; Vinay Singh
Sufficient optimality conditions are established for a class of nondifferentiable generalized minimax fractional programming problem with support functions. Further, two dual models are considered and weak, strong and strict converse duality theorems are established under the assumptions of (C,α,ρ,d)-convexity. Results presented in this paper, generalizes several results from literature to more general model of the problems as well as for more general class of generalized convexity. © 2014 Published by Elsevier B.V.
Optimality and duality for nonsmooth multiobjective optimization problems with generalized V-r-invexity
(2010) S.K. Mishra; Vinay Singh; S.Y. Wang; K.K. Lai
In this paper, a new concept of invexity for locally Lipschitz vector-valued functions is introduced, called V-r-type I functions. The generalized Karush-Kuhn-Tucker sufficient optimality conditions are proved and duality theorems are established for a nonsmooth multiobjective optimization problems involving V-r-type I functions with respect to the same function η. © de Gruyter 2010.
Optimality and duality for nonsmooth semi-infinite multiobjective programming with support functions
(Faculty of Organizational Sciences, Belgrade, 2017) Yadvendra Singh; S.K. Mishra; K.K. Lai
In this paper, we consider a nonsmooth semi-infinite multiobjective programming problem involving support functions. We establish sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and establish weak, strong and strict converse duality theorems under various generalized convexity assumptions. Moreover, some special cases of our problem and results are presented.