A trust region method for semi-infinite programming problems

We present a new successive quadratic programming (SQP) approach for semi-infinite programming problems with a trust region technique. Numerical methods for solving semi-infinite programming problems can be divided into continuous methods and discretization methods. We begin with a trust region method for nonlinear programming problems which possesses a fast and global convergence property and obviates the Maratos effect which is an unfavourable phenomenon that sometimes occurs for general SQP-type approaches. Then we apply the method to discretized semi-infinite programming problems by utilizing an L-infinity exact penalty function and epsilon-most-active constraints. The L-infinity exact penalty function is, in fact, essential for continuity methods for semi-infinite programming problems so as to maintain continuity of the exact penalty function, and enables the use of epsilon-most-active constraints in discretized semi-infinite programming problems. The results of preliminary computational experiments demonstrate the effectiveness of our approach for discretized semi-infinite programming problems.