The convergence of global search algorithm in the problem of convex maximization on admissible set (Q1589148)

The following nonconvex optimization problem (P) \(f(x) \to \max\), \(x \in D\) is studied, where \(f: \mathbb R^n \to \mathbb R \cup \{+\infty\}\) is a convex continuously differentiable function and \(D \subset \mathbb R^n\) is a convex set. In general, problem (P) has a number of local maxima, and there exist no simple and efficient algorithms for its solution. The authors give a construction to find the global maxima of problem (P) that can be used only in the case when at each iteration there is an algorithm for the solution of an auxiliary linear subproblem.