The Proximal Method of Multipliers for a Class of Nonsmooth Convex Optimizaiton

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  • TAKEUCHI Tomoya
    東京大学生産技術研究所　情報・エレクトロニクス系部門 東京大学大学院　数理科学研究科

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Other Title
  • 非平滑凸最適化問題に対する近接乗数法
  • The Proximal Method of Multipliers for a Class of Nonsmooth Convex Optimization

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Abstract

<p>We develop the theoretical foundation on the proximal method of multipliers for a class of nonsmooth convex optimization. The method generates a sequence of subproblems for the objective functions of the sum of the augmented Lagrangian due to Fortin and the proximal term. We show that the sequence of approximations to the subproblems converges to a saddle point of the standard Lagrangian even if the original optimization problem may possess multiple solutions. We employ a nonsmooth Newton method for computing an approximation to the subproblem. We exploit the theory of the nonsmooth analysis to provide a rigorous proof for the global convergence of the nonsmooth Newton algorithm.</p>

Journal

  • SEISAN KENKYU

    SEISAN KENKYU 70 (3), 157-164, 2018-05-01

    Institute of Industrial Science The University of Tokyo

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