Convergence qualification of adaptive partition algorithms in global optimization (Q1196187)

The author considers the optimization problem \(\min f(x)\), subject to \(x\in M\), where \(M\) is a bounded set, which is a closure of a non-empty open set of the real Euclidean \(n\)-space. The objective function \(f\) is continuous and may be multiextremal on \(M\). A general class of methods solving this problem via ``complete'' partition and search of \(M\) is investigated. Necessary and sufficient convergence conditions are formulated.