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Solving Infinite-dimensional Optimization Problems By Polynominal Approximation

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Executive Summary

In this paper, the authors solve a class of convex infinite-dimensional optimization problems using a numerical approximation method that does not rely on discretization. Instead, they restrict the decision variable to a sequence of finite-dimensional linear subspaces of the original infinite-dimensional space and solve the corresponding finite-dimensional problems in an efficient way using structured convex optimization techniques. They prove that, under some reasonable assumptions, the sequence of these optimal values converges to the optimal value of the original infinite-dimensional problem and give an explicit description of the corresponding rate of convergence.

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