A minimization method with approximation of feasible set and epigraph of objective function

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• 作者：I. Ya. Zabotin ; O. N. Shul’gina ; R. S. Yarullin
• 关键词：convex programming ; cutting ; plane methods ; approximating set ; cutting plane ; sequence of approximations ; convergence
• 刊名：Russian Mathematics (Iz VUZ)
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：60
• 期：11
• 页码：78-81
• 全文大小：488 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
• ISSN：1934-810X
• 卷排序：60

文摘

For a convex programming problem we propose a solution method which belongs to the class of cutting-plane methods. When constructing approximate solutions to the problem, this technique concurrently approximates its feasible set and the epigraph of the objective function. Planes for cutting the iteration points are being constructed with the help of subgradients of the objective function and left-hand sides of constraints. In this connection, one can find each iteration point by solving a linear programming problem. As distinct from most other well-known cuttingplane methods, the proposed technique allows the possibility to periodically update approximating sets by dropping accumulated constraints. We substantiate the convergence of the proposed method and discuss its numerical realization.