Transversality and Alternating Projections for Nonconvex Sets

被引：57
作者：
Drusvyatskiy, D. [1 ]
Ioffe, A. D. [2 ]
Lewis, A. S. [3 ]
机构：
[1] Univ Washington, Dept Math, Seattle, WA 98195 USA
[2] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel
[3] Cornell Univ, ORIE, Ithaca, NY 14853 USA
来源：
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS | 2015年 / 15卷 / 06期
基金：
美国国家科学基金会;
关键词：
Alternating projections; Linear convergence; Variational analysis; Slope; Transversality; CONVERGENCE; REGULARITY; MANIFOLDS; SARD;
D O I：
10.1007/s10208-015-9279-3
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear convergence. When the two sets are semi-algebraic and bounded, but not necessarily transversal, we nonetheless prove subsequence convergence.
引用
收藏
页码：1637 / 1651
页数：15
相关论文
共 35 条
  • [1] Alternating Projections on Nontangential Manifolds
    Andersson, Fredrik
    Carlsson, Marcus
    [J]. CONSTRUCTIVE APPROXIMATION, 2013, 38 (03) : 489 - 525
  • [2] [Anonymous], ARXIV150507920
  • [3] [Anonymous], 1993, Set-Valued Anal, DOI DOI 10.1007/BF01027691
  • [4] [Anonymous], 2002, RAAG Notes
  • [5] [Anonymous], 1965, Dokl. Akad. Naiik. USSR
  • [6] Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Lojasiewicz Inequality
    Attouch, Hedy
    Bolte, Jerome
    Redont, Patrick
    Soubeyran, Antoine
    [J]. MATHEMATICS OF OPERATIONS RESEARCH, 2010, 35 (02) : 438 - 457
  • [7] Restricted Normal Cones and the Method of Alternating Projections: Theory
    Bauschke, Heinz H.
    Luke, D. Russell
    Phan, Hung M.
    Wang, Xianfu
    [J]. SET-VALUED AND VARIATIONAL ANALYSIS, 2013, 21 (03) : 431 - 473
  • [8] Restricted Normal Cones and the Method of Alternating Projections: Applications
    Bauschke, Heinz H.
    Luke, D. Russell
    Phan, Hung M.
    Wang, Xianfu
    [J]. SET-VALUED AND VARIATIONAL ANALYSIS, 2013, 21 (03) : 475 - 501
  • [9] Bochnak J., 1998, REAL ALGEBRAIC GEOME
  • [10] Clarke subgradients of stratifiable functions
    Bolte, Jerome
    Daniilidis, Aris
    Lewis, Adrian
    Shiota, Masahiro
    [J]. SIAM JOURNAL ON OPTIMIZATION, 2007, 18 (02) : 556 - 572
1234