tailieunhanh - Mixed type symmetric and self duality for multiobjective variational problems with support functions

In this paper, a pair of mixed type symmetric dual multiobjective variational problems containing support functions is formulated. This mixed formulation unifies two existing pairs Wolfe and Mond-Weir type symmetric dual multiobjective variational problems containing support functions. | Yugoslav Journal of Operations Research 23 (2013) Number 3, 387-417 DOI: MIXED TYPE SYMMETRIC AND SELF DUALITY FOR MULTIOBJECTIVE VARIATIONAL PROBLEMS WITH SUPPORT FUNCTIONS Department of Mathematics, Jaypee University of Engineering and Technology, Guna, MP, India. Email: ihusain11@ Rumana, Department of Statistics, University of Kashmir, Srinagar, Kashmir, India. Email: rumana_research@ Received: May 2011 / Accepted: March 2013 Abstact: In this paper, a pair of mixed type symmetric dual multiobjective variational problems containing support functions is formulated. This mixed formulation unifies two existing pairs Wolfe and Mond-Weir type symmetric dual multiobjective variational problems containing support functions. For this pair of mixed type nondifferentiable multiobjective variational problems, various duality theorems are established under convexity-concavity and pseudoconvexity-pseudoconcavity of certain combination of functionals appearing in the formulation. A self duality theorem under additional assumptions on the kernel functions that occur in the problems is validated. A pair of mixed type nondifferentiable multiobjective variational problem with natural boundary values is also formulated to investigate various duality theorems. It is also pointed that our duality theorems can be viewed as dynamic generalizations of the corresponding (static) symmetric and self duality of multiobjective nonlinear programming with support functions. Kеywords: Efficiency, mixed type symmetric duality, mixed type self duality, natural boundary values, multiobjective nonlinear programming, convexity-convexity, pseudoconvexitypseudoconcavity, support functions. MSC: 90C30, 90C11, 90C20, 90C26. 388 , / Mixed Type Symmetric 1. INTRODUCTION Following Dorn [6], symmetric duality results in mathematical programming have been derived by a number of authors, notably, Dantzig et al [7], Mond .

• Toán học
• Mixed type symmetric duality
• Mixed type self duality
• Natural boundary values
• Multiobjective nonlinear programming
• Convexity convexity
• Support functions