A general duality scheme for nonconvex minimization problems with a strict inequality constraint
Let \(g\) and \(k\) be two extended-real-valued convex functions defined over a locally convex topological vector space \(X\). Let \(f\) and \(h\) belong to the class of functions on \(X\) that can be written as lower envelope of an arbitrary family of convex functions. The authors establish a duality formula for the minimization problem: \[ \text{minimize }\{f(x)+ g(x)\text{ subject to } h(x) +k(x)<0\}. \] Applications in D.C. and Lipschitzian optimization are considered. The present paper is an extension of a previous work by the same authors [Nonconvex Optimization and Its Applications 27, 331-345 (1998)].
scientific article; zbMATH DE number 1228658