TAILIEUCHUNG - Efficiency and duality in nonsmooth multiobjective fractional programming involving η - pseudolinear functions

In this paper, we shall establish necessary and sufficient conditions for a feasible solution to be efficient for a nonsmooth multiobjective fractional programming problem involving η − pseudolinear functions. Furthermore, we shall show equivalence between efficiency and proper efficiency under certain boundedness condition. | Yugoslav Journal of Operations Research 22 (2012), Number 1, 3-18 DOI: EFFICIENCY AND DUALITY IN NONSMOOTH MULTIOBJECTIVE FRACTIONAL PROGRAMMING INVOLVING η -PSEUDOLINEAR FUNCTIONS S. K. MISHRA, Department of Mathematics Faculty of Science Banaras Hindu University, Varanasi-221005, India B. B. UPADHYAY1 Department of Mathematics Faculty of Science Banaras Hindu University, Varanasi- 221005, India Received: December 2010 / Accepted: December 2011 Abstract: In this paper, we shall establish necessary and sufficient conditions for a feasible solution to be efficient for a nonsmooth multiobjective fractional programming problem involving η − pseudolinear functions. Furthermore, we shall show equivalence between efficiency and proper efficiency under certain boundedness condition. We have also obtained weak and strong duality results for corresponding Mond-Weir subgradient type dual problem. These results extend some earlier results on efficiency and duality to multiobjective fractional programming problems involving pseudolinear and η − pseudolinear functions. Keywords: Multiobjective fractional programming, nonsmooth programming, pseudolinearity, η − pseudolinearity, duality. MSC: 90C32; 49J52; 52A01. 1 This author is supported by the Council of Scientific and Industrial Research, New Delhi, India, through grant no. 09/013(0357)/2011-EMR-I. 4 . Mishra, . Upadhyay / Efficiency And Duality In Nonsmooth 1. INTRODUCTION In the optimization theory, convexity and its different generalizations play an important role. Mangasarian [16] introduced the concept of pseudoconvex functions as a generalization of the convex functions. Chew and Choo [5] introduced a new class of functions both pseudoconvex and pseudoconcave known as pseudolinear functions. Chew and Choo [5] obtained first and second order characterizations for pseudolinear functions. Komlosi [11] and Rapcsak [22] studied and characterized higher .

• Toán học
• Multiobjective fractional programming
• Nonsmooth programming
• η − pseudolinearity
• Pseudolinear functions
• Involving pseudolinear
• D type I n set functions
• Multiobjective programming
• Duality results
• Multiobjective nonlinear fractional programming problem
• Optimization problems
• Clarke gradient
• Sufficient optimality conditions
• Duality theorems
• Multiobjective nonlinear programming
• Sum of ratio
• Multiobjective linear fractional programming
• Optimality and duality
• Saddle point criteria
• Higher order duality
• Support function
• Generalized convexity
• Convex transformations