Global convergence of a semi-infinite optimization method (Q912572)

The author presents and establishes the convergence of an algorithm for minimizing locally Lipschitz functions using approximate function values. The algorithm is an extension of the trust region methods used in composite nondifferentiable optimization. The author implements his algorithm for the semi-infinite programming problem Minimize \(f(x)\) over \(x\in R^ n\) subject to \(g(x,s)\leq 0\) for all \(s\in [0,1],\) where \(f: R^ n\to R\) and \(g: R^ n\times R\to R\) are smooth functions. Preliminary numerical testing, presented in the paper, shows the algorithm to be effective in solving semi-infinite programming problems.