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Das, Prasanta Kumar The Youngnam Mathematical Society 2017 East Asian mathematical journal Vol.33 No.1
The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.
Prasanta Kumar Das 영남수학회 2017 East Asian mathematical journal Vol.33 No.1
The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized op- timization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, P DA- vector function and P DA-antisymmetric function to show the exis- tence of a new class of function called, (Tη;ξθ)-invex functions. We discuss first and second kind of (Tη;ξθ)-invex functions and establish their exis- tence theorems in ordered topological vector spaces.
DUALITY THEOREM AND VECTOR SADDLE POINT THEOREM FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEM
KIM, MOON HEE 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.18 No.1
In this paper, sufficient optimality conditions and duality results for nonsmooth vector optimization problems are given under near invexity and infineness assumptions. Also, weak vector saddle-point theorems are obtained under near invexity-infineness assumptions.
DUALITY THEOREM AND VECTOR SADDLE POINT THEOREM FOR ROBUST MULTIOBJECTIVE OPTIMIZATION PROBLEMS
Kim, Moon Hee Korean Mathematical Society 2013 대한수학회논문집 Vol.28 No.3
In this paper, Mond-Weir type duality results for a uncertain multiobjective robust optimization problem are given under generalized invexity assumptions. Also, weak vector saddle-point theorems are obtained under convexity assumptions.
ROBUST DUALITY FOR GENERALIZED INVEX PROGRAMMING PROBLEMS
Kim, Moon Hee Korean Mathematical Society 2013 대한수학회논문집 Vol.28 No.2
In this paper we present a robust duality theory for generalized convex programming problems under data uncertainty. Recently, Jeyakumar, Li and Lee [Nonlinear Analysis 75 (2012), no. 3, 1362-1373] established a robust duality theory for generalized convex programming problems in the face of data uncertainty. Furthermore, we extend results of Jeyakumar, Li and Lee for an uncertain multiobjective robust optimization problem.