The relief indicator method for constrained global optimization

The authors consider the problem of globally minimizing a continuous, not-necessarily smooth function f(x) over a compact set S in . To each real number they associate a function , called the relief indicator, such that the function is closed, convex, and a feasible point is a global optimal solution if and only if where. Based on this global optimality criterion, an algorithm is then developed which reduces the problem to a sequence of linearly constrained concave quadratic separable programs. The authors discuss the practical use of these results when n (the number of variables) is small and also show how the method can be applied in the decomposition of certain nonconvex problems.