Norma G. Rueda

Optimality and duality with generalized convexity

Hanson and Mond have given sets of necessary and sufficient conditions for optimality and duality in constrained optimization by introducing classes of generalized convex functions, called type I and type II functions. Recently, Bector defined univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, optimality and duality results for several mathematical programs are obtained combining the concepts of type I and univex functions. Examples of functions satisfying these conditions are given.

Higher-order generalized invexity and duality in nondifferentiable mathematical programming

In this paper we consider a number of higher-order duals to a nondifferentiable programming problem and establish duality under the higher-order generalized invexity conditions introduced in an earlier work by Mishra and Rueda.

Sufficiency and duality for multiobjective control problems under generalized (B, ρ)-type I functions

In this paper, we introduce the classes of (B, ρ)-type I and generalized (B, ρ)-type I, and derive various sufficient optimality conditions and mixed type duality results for multiobjective control problems under (B, ρ)-type I and generalized (B, ρ)-type I assumptions.

Duality in nonlinear multiobjective programming using augmented Lagrangian functions

A vector-valued generalized Lagrangian is constructed for a nonlinear multiobjective programming problem. Using the Lagrangian, a multiobjective dual is considered. Without assuming differentiability, weak and strong duality theorems are established using Pareto efficiency.

Symmetric duality for mathematical programming in complex spaces with F-convexity

Abstract Under F -convexity, F -concavity/ F -pseudoconvexity, F -pseudoconcavity, appropriate duality results for a pair of Wolfe and Mond–Weir type symmetric dual nonlinear programming problems in complex spaces are established. These results are then used to develop second order F -convexity, F -concavity, second order F -pseudoconvexity, F -pseudoconcavity, and appropriate second order symmetric dual nonlinear programming problems in complex spaces.

Generalized invexity-type conditions in constrained optimization

This paper defines a new class of generalized type I functions, and obtains Kuhn-Tucker necessary and sufficient conditions and duality results for constrained optimization problems in the presence of the aforesaid weaker assumptions on the objective and constraint functions involved in the problem.

Fritz john second-order duality for nonlinear programming

Abstract A second-order dual to a nonlinear programming problem is formulated. This dual uses the Fritz John necessary optimality conditions instead of the Karush-Kuhn-Tucker necessary optimality conditions, and thus, does not require a constraint qualification. Weak, strong, strict-converse, and converse duality theorems between primal and dual problems are established.