Duality Theorems for a Class of Nonconvex Vector Optimization Programming in Banach Spaces
Rui Peng · Journal of Sichuan Normal University · 2012
In this paper,a class of nonconvex vector optimization programming in general Banach spaces is discussed.A Mond-Weir-Like dual mathematical programming problem for a class of nonconvex vector optimization programming in Banach spaces is proposed on the basis of some scholars' research results.Some new weak(strong) duality results are obtained by means of their inherent properties and by using an invexity notion for mappings defined between Banach spaces.The proposed weak(strong) duality results have been strictly shown under a Slater-type constraint qualification condition.We obtain some new weak(strong) duality results on which a class of multiobjective optimization problem is defined on general Banach spaces,and the objective and constraint functions are nondifferentiable strongly compact Lipschitz.