Study of duality in non differentiable multi objective variationed problem

Abstract

newlineThe concept of invariant monotonicity and generalized invariant monotonicity with newlineconvex and invex functions have been widely used and receiving attention as far as newlinemultobjective variational problems for non-differentiable functions are involved. Most newlinetasks in optimization theory deals with continuous non-differentiable problems. In fact in newlinethe last few years several research papers containing variational problems have been newlinepublished. newlineThis thesis investigate the transformation of some paper of R.N. MUKHERJEE newlineand S.K. MISHRA and others on non-differentiable variational programming problems in newlineand#961; and#61485; and#61480;and#951;,and#952;and#61481; invexity framework. The research work based on multiobjective variational newlineproblems is studied in different type of invexity frame work. Further in this thesis, we newlinehave generalized the idea of J-Sandoor to the properties B-subadditivity and newlineAntisymmetricity, B-decreasing and A-Convexity. newlineChapter-1 is an introductory and contains brief history of non-differentiable multiobjective newlineprogramming problems involving invexity and sub-additivity. newlineChapter-2 describes pre-requisites for study of non differentiable multi-objective newlinevariational problems. newlineChapter-3 deals with Generalized Invexity and Invariant. Relationships between newlinegeneralized invariant monotonicities and generalized invexity has been established. newlineChapter- 4 deals with A Note on Subadditivity and Antisymmetricity Involving newlineGeneralized Convex Functions. newlineChapter 5 deals with On Nondifferentiable Multiobjective Programming Involving Type- newlineI and#945;-Invex Functions. newlineChapter 6 is devoted on a class of generalized convex functions with some applications. newlineIn this chapter we have generalized the notation of B-subadditivity, Antisymmitricity, Aconvexity, newlineand#61544;-invexity and studied their properties in different theorems. newlineChapter 7 deals with the idea of anti-symmetricity in n-dimension and effectively applied newlineit to prove theorems on sub-additivity, A-convexity and B-decreasing properties of newlinefunctions. newlinevii newlineChapter 8 deals with Multiobjective Duality with and#961; and#61485; and#61480;and#951;,and#952;and#61481; -invexity.