A Fritz John optimality condition using the approximate subdifferential
The main result of the paper is the derivation of a Fritz John type first-order optimality condition for the following optimization problem: (P) \(\min f(x)\) s.t. \(-g(x)\in S\). Here \(X\) and \(Y\) are Banach spaces, \(Y\) is separable, \(S\subset Y\) is a closed convex cone, \(f: X\to R\) and \(g: X\to Y\) are locally Lipschitz functions. An additional assumption on \(S\) is made in order to derive the conditions for optimality: either the interior of \(S\) is not empty or \(Y\) is finite-dimensional. Instead of using the Clarke subdifferential to establish the optimality conditions, the authors use the approximate subdifferential. A discussion of the properties of the approximate subdifferential for locally Lipschitz functions is included.
Fritz John type first- order optimality condition
scientific article; zbMATH DE number 638719
scientific article