Generalized Preinvexity and Second Order Duality in Multiobjective Programming

Description

This book introduces readers to several new generalized preinvex functions and generalized invariant monotone functions. It begins by describing the main properties of these functions and various relations. Several examples are then presented to illustrate various interesting relationships among preinvex functions and the properly inclusive relations among the generalized invariant monotonicities. In addition, several second order and higher order symmetric duality models are provided for multi-objective nonlinear programming problems. Lastly, weak and strong duality theorems under generalized convexity assumptions are provided. The book offers a well-synthesized, accessible, and usable treatment for students, researchers and practitioners in the areas of OR, optimization, applied mathematics and engineering, and all those working on a wide range of related problems, which include financial institutions, logistics, transportation, traffic management, etc. Front Matter ....Pages i-xii Front Matter ....Pages 1-1 Preinvex Functions (Xinmin Yang)....Pages 3-20 Semistrictly Preinvex Functions (Xinmin Yang)....Pages 21-41 Semipreinvex Functions (Xinmin Yang)....Pages 43-52 Prequasiinvex Functions (Xinmin Yang)....Pages 53-74 Front Matter ....Pages 75-75 Generalized Invexity and Generalized Invariant Monotonicity (Xinmin Yang)....Pages 77-91 Front Matter ....Pages 93-93 Multiobjective Wolfe Type Second-Order Symmetric Duality (Xinmin Yang)....Pages 95-107 Multiobjective Mond-Weir-Type Second-Order Symmetric Duality (Xinmin Yang)....Pages 109-120 Multiobjective Second-Order Duality with Cone Constraints (Xinmin Yang)....Pages 121-148 Multiobjective Higher-Order Duality (Xinmin Yang)....Pages 149-158 Back Matter ....Pages 159-167