Strong pseudo-convexity and symmetric duality in nonlinear programming

Abstract

In this note, the weak duality theorem of symmetric duality in nonlinear programming and some related results are established under weaker (strongly Pseudo-convex/strongly Pseudo-concave) assumptions. These results were obtained by Bazaraa and Goode [1] under (stronger) convex/concave assumptions on the function.

Symmetric and Asymmetric Duality

“…where C 1 and C 2 are closed convex cones with nonempty interior and the 0 denotes the positive polar; in [7] the convexity assumptions are weakened with the hypotheses of pseudoconvexity but another feasibility assumption is added. This result cannot be generalized to the case of quasiconvexity; in fact if we consider K x ω = x − 1 3 , we obtain v SP = −1 and v SD = 0.…”

“…In [4], in fact, a symmetric duality scheme is formulated (in the sense that the feasible regions of the two problems, primal and dual, are contained in spaces having the same dimension) and a weak duality theorem, under the hypotheses of convexity and differentiability for the considered functions is established. Such a scheme has been generalized to the pseudoconvex [7] and to the pseudoinvex [9] case.…”