Convergence of the gradient projection method and Newton’s method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set

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• 作者：Yu. A. Chernyaev
• 关键词：spherical surface ; convex closed set ; gradient projection method ; Newton’s method ; necessary conditions for a local minimum ; convergence of an algorithm
• 刊名：Computational Mathematics and Mathematical Physics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：56
• 期：10
• 页码：1716-1731
• 全文大小：377 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1555-6662
• 卷排序：56

文摘

The gradient projection method and Newton’s method are generalized to the case of nonconvex constraint sets representing the set-theoretic intersection of a spherical surface with a convex closed set. Necessary extremum conditions are examined, and the convergence of the methods is analyzed.