A Subspace Version of the Powell–Yuan Trust-Region Algorithm for Equality Constrained Optimization

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• 作者：Geovani Nunes Grapiglia (1) (2)
  Jinyun Yuan (1)
  Ya-xiang Yuan (3)
  
• 关键词：Constrained optimization ; Trust ; region methods ; Subspace methods ; 90C30 ; 90C53 ; 49M37
• 刊名：Journal of the Operations Research Society of China
• 出版年：2013
• 出版时间：December 2013
• 年：2013
• 卷：1
• 期：4
• 页码：425-451
• 全文大小：925 KB
• 作者单位：Geovani Nunes Grapiglia (1) (2)
  Jinyun Yuan (1)
  Ya-xiang Yuan (3)
  
  1. Departamento de Matemática, Universidade Federal do Paraná, Centro Politécnico, Cx. postal 19.081, 81531-980, Curitiba, Paraná, Brazil
  2. The Capes Foundation, Ministry of Education of Brazil, Cx. postal 250, 70.040-020, Brasília, Distrito Federal, Brazil
  3. State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Zhongguancundonglu 55, Beijing, 100190, P.R. China
  
• ISSN：2194-6698

文摘

This paper studied subspace properties of the Celis–Dennis–Tapia (CDT) subproblem that arises in some trust-region algorithms for equality constrained optimization. The analysis is an extension of that presented by Wang and Yuan (Numer. Math. 104:241-69, 2006) for the standard trust-region subproblem. Under suitable conditions, it is shown that the trial step obtained from the CDT subproblem is in the subspace spanned by all the gradient vectors of the objective function and of the constraints computed until the current iteration. Based on this observation, a subspace version of the Powell–Yuan trust-region algorithm is proposed for equality constrained optimization problems where the number of constraints is much lower than the number of variables. The convergence analysis is given and numerical results are also reported.