首页 | 本学科首页   官方微博 | 高级检索  
     


Continuity of the null space basis and constrained optimization
Authors:Richard H. Byrd  Robert B. Schnabel
Affiliation:(1) Department of Computer Science, University of Colorado, 80309 Boulder, USA
Abstract:Many constrained optimization algorithms use a basis for the null space of the matrix of constraint gradients. Recently, methods have been proposed that enable this null space basis to vary continuously as a function of the iterates in a neighborhood of the solution. This paper reports results from topology showing that, in general, there is no continuous function that generates the null space basis of all full rank rectangular matrices of a fixed size. Thus constrained optimization algorithms cannot assume an everywhere continuous null space basis. We also give some indication of where these discontinuities must occur. We then propose an alternative implementation of a class of constrained optimization algorithms that uses approximations to the reduced Hessian of the Lagrangian but is independent of the choice of null space basis. This approach obviates the need for a continuously varying null space basis.Research supported by NSF grant MCS 81-15475 and DCR-8403483Research supported by ARO contracts DAAG 29-81-K-0108 and DAAG 29-84-K-0140
Keywords:Null space basis  QR factorization  constrained optimization  reduced Hessian
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号