On strong pseudoconvexity in nonlinear programming duality (Q750300)

Let S be an open convex set in \(R^ n\) and let f: \(S\to R\) be differentiable. If there exists an arbitrary positive functional p: \(S\times S\to R\) satisfying f(y)-f(x)\(\geq p(x,y)(y-x)^ T\nabla f(x,y)\) for all x,y\(\in S\), then f is said to be strongly pseudoconvex with respect to p(x,y) over s. Clearly, strong pseudoconvexity is a weaker condition than convexity but stronger than pseudoconvexity. The author proves duality theorems for a pair of dual programs first introduced by \textit{B. Mond} and himself [in: Generalized concavity in optimization and economics, Proc. NATO Adv. Study Inst., Vancouver/Can. 1980, 263-279 (1981; Zbl 0538.90081)] under the strong pseudoconvexity assumption on the constraint function.