Optimal solution approximation for infinite positive-definite quadratic programming |
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| Authors: | P Benson R L Smith I E Schochetman J C Bean |
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| Institution: | (1) Rubicon, Ann Arbor, Michigan;(2) Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan;(3) Department of Mathematical Sciences, Oakland University, Rochester, Michigan;(4) Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan |
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| Abstract: | We consider a general doubly-infinite, positive-definite, quadratic programming problem. We show that the sequence of unique optimal solutions to the natural finite-dimensional subproblems strongly converges to the unique optimal solution. This offers the opportunity to arbitrarily well approximate the infinite-dimensional optimal solution by numerically solving a sufficiently large finite-dimensional version of the problem. We then apply our results to a general time-varying, infinite-horizon, positive-definite, LQ control problem.This work was supported in part by the National Science Foundation under Grants ECS-8700836, DDM-9202849, and DDM-9214894. |
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| Keywords: | Time-varying systems positive-definite costs infinite-horizon optimization infinite quadratic programming solution approximations LQ control problems |
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