Solving infinite-dimensional optimization problems by polynomial approximation
(2010) Recent Advances in Optimization and its Applications in Engineering — ISBN: [978-3-642-12597-3], p. 37-46, published
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- Abstract
- 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 an 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. In M. Diehl, F. Glineur, E. Jarlebring and W. Michiels (ed.), Recent Advances in Optimization and its Applications in Engineering (p. p. 37-46). Springer. https://doi.org/10.1007/978-3-642-12598-0_3