tailieunhanh - Sufficient optimality conditions and duality for nonsmooth multiobjective optimization problems via higher order strong convexity

In this paper, we define some new generalizations of strongly convex functions of order m for locally Lipschitz functions using Clarke subdifferential. Suitable examples illustrating the non emptiness of the newly defined classes of functions and their relationships with classical notions of pseudoconvexity and quasiconvexity are provided. | Yugoslav Journal of Operations Research 27 (2017), Number 2, 227–242 DOI: SUFFICIENT OPTIMALITY CONDITIONS AND DUALITY FOR NONSMOOTH MULTIOBJECTIVE OPTIMIZATION PROBLEMS VIA HIGHER ORDER STRONG CONVEXITY Balendu B. UPADHYAY Department of Mathematics National Institute of Technology, Manipur, Imphal-795004, INDIA bhooshan@ Ningthoujam PRIYOBARTA Department of Mathematics National Institute of Technology, Manipur, Imphal-795004, INDIA ningthoujampriyo9@ Yumnam S. ROHEN Department of Mathematics National Institute of Technology, Manipur, Imphal-795004, INDIA ymnehor2008@ Received: January 2017 / Accepted: May 2017 Abstract: In this paper, we define some new generalizations of strongly convex functions of order m for locally Lipschitz functions using Clarke subdifferential. Suitable examples illustrating the non emptiness of the newly defined classes of functions and their relationships with classical notions of pseudoconvexity and quasiconvexity are provided. These generalizations are then employed to establish sufficient optimality conditions for a nonsmooth multiobjective optimization problem involving support functions of compact convex sets. Furthermore, we formulate a mixed type dual model for the primal problem and establish weak and strong duality theorems using the notion of strict efficiency of order m. The results presented in this paper extend and unify several known results from the literature to a more general class of functions as well as optimization problems. Keywords: Nonsmooth Multiobjective Programming, Support Functions, Strict Minimizers, Optimality Conditions, Mixed Duality. 228 B. Upadhyay, , . Rohen / Sufficient Optimality Conditions MSC: 90C29, 90C46, 49N15. 1. INTRODUCTION The nonsmooth phenomena occur naturally and frequently in optimization theory. This led to the introduction of several types of generalized directional derivatives and .

• Toán học
• Nonsmooth multiobjective programming
• Support functions
• Strict minimizers
• Optimality conditions
• Mixed dualit
• Nonsmooth semi infinite
• Multiobjective Optimization
• Generalized convexity
• Multiobjective programming
• Multiobjective fractional programming
• Nonsmooth programming
• η − pseudolinearity
• Pseudolinear functions
• Involving pseudolinear
• Clarke gradient
• Sufficient optimality conditions
• Duality theorems
• Multiobjective nonlinear programming