On outer approximation methods for solving concave minimization problems (Q1063521)

This paper first considers the following global optimization problem: (P) minimize f(x), subject to \(x\in D\), where \(f:R^ n\to R\) is a real- valued concave function defined throughout \(R^ n\), and D is a closed convex subset of \(R^ n\), and discuss the outer approximation methods for solving (P). Basically, these methods consist in approximating the set D by a polyhedral convex set containing it. The main aim of this paper is to provide a unifying scheme which could be applied to a wider class of problems, where the constraint set may be unbounded or even nonconvex of a certain type.