Generalized Preinvexity and Second Order Duality in Multiobjective Programming

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.

Introduces generalized convex functions and generalized monotone functions Equips readers with generalized preinvex functions and generalized invariant monotonicities Application to the study of optimality conditions and duality theory in optimization

Contenu
Preinvex Functions.- Semistrictly Preinvex Functions.- Semipreinvex Functions.- Prequasiinvex Functions.- Generalized Invexity and Generalized Invariant Monotonicity.- Multiobjective Wolfe Type Second-Order Symmetric Duality.- Multiobjective Mond-Weir Type Second Order Symmetric Duality.- Multiobjective Second Order Duality with Cone Constraints.