TAILIEUCHUNG - Higher order duality in multiobjective fractional programming problem with generalized convexity

This paper, motivated by the earlier works on higher order duality, we first introduce one new generalized invex function . The sufficient optimality conditions have also been derived and duality results have been estabilished for Schaible type dual of a nondifferentiable multiobjective fractional programming problem. | Yugoslav Journal of Operations Research 27 (2017), Number 2, 249–264 DOI: HIGHER ORDER DUALITY IN MULTIOBJECTIVE FRACTIONAL PROGRAMMING PROBLEM WITH GENERALIZED CONVEXITY PANKAJ Mahila Maha Vidhyalaya, Banaras Hindu University, Varanasi-221005, India pankaj22iitr@ Bhuwan Chandra JOSHI DST-Centre for Interdisciplinary Mathematical Sciences, Faculty of Science, Banaras Hindu University, Varanasi-221005, India bhuwanjoshi007@ Received: January 2017 / Accepted: May 2017 ˜ r˜ -invex Abstract: We have introduced higher order generalized hybrid B − b, ρ, θ, p, function. Then, we have estabilished higher order weak, strong and strict converse duality theorems for a multiobjective fractional programming problem with support function in the numerator of the objective function involving higher order generalized hybrid ˜ r˜ -invex functions. Our results extend and unify several results from the B − b, ρ, θ, p, literature. Keywords: Multiobjective Fractional Programming, Support Function, Duality, Higher ˜ r˜ -invex Function. Order B − b, ρ, θ, p, MSC: 90C26, 90C29, 90C32, 90C46. 1. INTRODUCTION In the last three decades, several definitions extending the concept of convexity of a function have been introduced by many researchers including Schmitendorf [17], Vial [21], Hanson and Mond [6], Rueda and Hanson [16], Preda [14], and Antczak [1]. A significant generalization of convex function is introduced by Hanson [5] and Cravan [2]. In 1981, Hanson [5] generalized the Karush-Kuhn-Tucker type sufficient optimality conditions with the help of a new class of generalized 250 Pankaj, / Higher Order Duality convex functions for differentiable real valued functions which are defined on Rn . This class of functions was later named by Cravan [2] as the class of “invex” functions due to their property of invariance under convex transformations. Duality for nonlinear programming was studied by many researchers.

• Toán học
• Higher order duality
• Multiobjective fractional programming
• Support function
• Generalized convexity
• Convex transformations
• Higher order η – bonvexity
• Strict minimizers
• Second order dualit
• Mond Weir type dual
• Non differentiable multiobjective optimization problem
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• cách trình bày báo cáo
• báo cáo khoa học
• Nonsmooth multiobjective programming
• Support functions
• Optimality conditions
• Mixed dualit