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Solving infinite-dimensional optimizaiton problems by polynomial approximation

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  • DEVOLDER, Olivier
  • GLINEUR, François
  • NESTEROV, Yurii

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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Suggested Citation

  • DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2010. "Solving infinite-dimensional optimizaiton problems by polynomial approximation," LIDAM Reprints CORE 2241, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2241
    Note: In : M. Diehl, F. Glineur, E. Jarlebring and W. Michiels (eds.), Recent Advances in Optimization and its Applications in ENgineering, Heidelberg, Springer, 37-46, 2010
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    2. Jubril, A.M. & Olaniyan, O.A. & Komolafe, O.A. & Ogunbona, P.O., 2014. "Economic-emission dispatch problem: A semi-definite programming approach," Applied Energy, Elsevier, vol. 134(C), pages 446-455.
    3. Kristina Rognlien Dahl, 2019. "A convex duality approach for pricing contingent claims under partial information and short selling constraints," Papers 1902.10492, arXiv.org.
    4. Kristina Rognlien Dahl, 2019. "Management of a hydropower system via convex duality," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(1), pages 43-71, February.

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