The Institute of Statistical Mathematics

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The purpose of this research project is to develop efficient numerical methods, with a software package, for generalized semi-infinite programming (SIP). Numerical methods developed in this project include (1) an algorithm based on duality theory for solving convex SIP problems, (2) an algorithm based on local reduction within a framework of sequential quadratic programming for solving nonlinear SIP problems, (3) an algorithm based on nondifferentiable optimization theory for solving nonlinear SIP problems. We have also implemented (4) an approximation algorithm based on cutting plane strategy and (5) a two-phase algorithm based on cutting plane and local reduction. Also as further research directions, we have investigated (6) a path-following algorithm. based on continuous descent methods, together with related stiff systems of ordinary differential equations, and (7) numerical methods based on semi definite programming relaxations. Some of these numerical algorithms have been implemented and applied to problems of optimal filter design, global optimization, min-max programming, infinite games and optimal control, and these are now being compiled into a software package written in the Matlab environment, which will soon become available through our web site.