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Solving Infinite-dimensional Optimization Problems by Polynomial Approximation

Olivier Devolder (Olivier.devolder***at***uclouvain.be)
François Glineur (Francois.Glineur***at***uclouvain.be)
Yurii Nesterov (Yurii.Nesterov***at***uclouvain.be)

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 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.

Keywords: infinite-dimensional optimization, polynomial approximation, semidefinite programming, positive polynomials, optimization in normed spaces, continuous linear programs, infinite programming

Category 1: Infinite Dimensional Optimization

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Solving Infinite-dimensional Optimization Problems by Polynomial Approximation, Olivier Devolder, François Glineur, Yurii Nesterov, in Recent Advances in Optimization and its Applications in Engineering, Springer, 2010, pp. 31-40. http://dx.doi.org/10.1007/978-3-642-12598-0_3

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Entry Submitted: 08/03/2010
Entry Accepted: 08/03/2010
Entry Last Modified: 05/26/2011

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