Globally and superlinearly convergent trust-region algorithm for convex SC1-minimization problems and its application to stochastic programs

A function mapping from ⁿ to is called an SC¹-function if it is differentiable and its derivative is semismooth. A convex SC¹-minimization problem is a convex minimization problem with an SC¹-objective function and linear constraints. Applications of such minimization problems include stochastic quadratic programming and minimax problems. In this paper, we present a globally and superlinearly convergent trust-region algorithm for solving such a problem. Numerical examples are given on the application of this algorithm to stochastic quadratic programs.This work was supported by the Australian Research Council.We are indebted to Dr. Xiaojun Chen for help in the computation. We are grateful to two anonymous referees for their comments and suggestions, which improved the presentation of this paper.