A Cutting Plane Approach to Solving Quadratic Infinite Programs on Measure Spaces

Authors:
S. Y. Wu
Affiliations:
Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan (e-mail: soonyi@mail.ncku.edu.tw)
Venue:
Journal of Global Optimization
Year:
2001

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Abstract

We study infinite dimensional quadratic programming (QP) problems of integral type. The decision variable is taken in the space of bounded regular Borel measures on compact Hausdorff spaces. An implicit cutting plane algorithm is developed to obtain an optimal solution of the infinite dimensional QP problem. The major computational tasks in using the implicit cutting plane approach to solve infinite dimensional QP problems lie in finding a global optimizer of a non-linear and non-convex program. We present an explicit scheme to relax this requirement and to get rid of the unnecessary constraints in each iteration in order to reduce the size of the computatioinal programs. A general convergence proof of this approach is also given.