Convergence of a hybrid projection-proximal point algorithm coupled with approximation methods in convex optimization

• 成果类型: Article
• 署名作者: Alvarez, F; Carrasco, M; Pichard, K
• 署名单位: Universidad de Chile; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1050.0156
• 发表日期: 2005
• 页码: 966-984
• 关键词: exponential penalty; asymptotic analysis; monotone-operators; minimization; Penalization; trajectories; path

摘要

In order to minimize a closed convex function that is approximated by a sequence of better behaved functions, we investigate the global convergence of a general hybrid iterative algorithm, which consists of an inexact relaxed proximal point step followed by a suitable orthogonal projection onto a hyperplane. The latter permits to consider a fixed relative error criterion for the proximal step. We provide various sets of conditions ensuring the global convergence of this algorithm. The analysis is valid for nonsmooth data in infinite-dimensional Hilbert spaces. Some examples are presented, focusing on penalty/barrier methods in convex programming. We also show that some results can be adapted to the zero-finding problem for a maximal monotone operator.