Solving infinite-dimensional optimization problems by polynomial approximation
(2010)
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- Abstract
- In this paper, we solve a class of convex infinite-dimensional optimization problems using a numerical approximation method that does not rely on discretization. Instead, we 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 a efficient way using structured convex optimization techniques. We 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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Citations
Devolder, O., Glineur, F., & Nesterov, Y. (2010). Solving infinite-dimensional optimization problems by polynomial approximation (CORE Discussion Paper 2010/29). https://hdl.handle.net/2078.5/130946