Abstract
This chapter discusses the relationships between the nonlinear programs, as well as duality formulation in nonlinear programming. The duality theory in nonlinear programming is a natural extension of duality in linear programming. Several authors are interested in generalizing the well known duality properties of linear programs to nonlinear cases. The Lagrangian saddle point problem and the Kuhn–Tucker theory also incited a great deal of interest in duality in nonlinear programming. As a result, a large number of papers on duality in nonlinear programming appeared in the literature. Several duality formulations have been evolved by various authors under different conditions that satisfy many of the properties of linear dual programs. The chapter also provides the proofs of several duality theorems. Several approaches to duality formulation in nonlinear programming are available in the literature. To find early results on duality the chapter suggests to go through the versatile literature of Dennis, Dora, Wolfe, Hanson, and Mangasarian.
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