期刊名称：CORE Discussion Papers / Center for Operations Research and Econometrics (UCL), Louvain
出版年度：2010
卷号：2010
期号：1
出版社：Center for Operations Research and Econometrics (UCL), Louvain
摘要：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.
关键词：Keywords: infinite-dimensional optimization, polynomial approximation, semidefinite programming,
positive polynomials, optimization in normed spaces, continuous linear programs, infinite programming.
