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http://dx.doi.org/10.7858/eamj.2017.009

ON OPTIMALITY OF GENERALIZED OPTIMIZATION PROBLEMS ASSOCIATED WITH OPERATOR AND EXISTENCE OF (Tη; ξθ)-INVEX FUNCTIONS  

Das, Prasanta Kumar (Department of Mathematics KIIT University)
Publication Information
East Asian mathematical journal / v.33, no.1, 2017 , pp. 83-102 More about this Journal
Abstract
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.
Keywords
Generalized optimization problems; sufficient optimality theorem; weak duality theorem; strong duality theorem; ($T_{\eta}; {\xi}_{\theta}$)-invexity of first and second kind; (PDA)-operator; PDA-vector function and PDA-antisymmetric function;
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