Primal Central Paths and Riemannian Distances for Convex Sets

被引：0
|
作者：
Y. Nesterov
A. Nemirovski
机构：
[1] Catholic University of Louvain,CORE
[2] Technion-Israel Institute of Technology,undefined
来源：
Foundations of Computational Mathematics | 2008年 / 8卷
关键词：
Riemannian geometry; Convex optimization; Structural optimization; Interior-point methods; Path-following methods; Self-concordant functions; Polynomial-time methods; 52A41; 53C22; 68Q25; 90C22; 90C25; 90C51; 90C60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we study the Riemannian length of the primal central path in a convex set computed with respect to the local metric defined by a self-concordant function. Despite some negative examples, in many important situations, the length of this path is quite close to the length of a geodesic curve. We show that in the case of a bounded convex set endowed with a ν-self-concordant barrier, the length of the central path is within a factor O(ν1/4) of the length of the shortest geodesic curve.
引用
收藏
页码：533 / 560
页数：27
相关论文
共 50 条
  • [1] Primal central paths and Riemannian distances for convex sets
    Nesterov, Y.
    Nemirovski, A.
    [J]. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2008, 8 (05) : 533 - 560
  • [2] Distances to convex sets
    Granero, Antonio S.
    Sanchez, Marcos
    [J]. STUDIA MATHEMATICA, 2007, 182 (02) : 165 - 181
  • [3] SHORTEST PATHS IN GRAPHS OF CONVEX SETS
    Marcucci, Tobia
    Umenberger, Jack
    Parrilo, Pablo
    Tedrake, Russ
    [J]. SIAM JOURNAL ON OPTIMIZATION, 2024, 34 (01) : 507 - 532
  • [4] REGULAR SYSTEMS OF PATHS AND FAMILIES OF CONVEX SETS IN CONVEX POSITION
    Dobbins, Michael Gene
    Holmsen, Andreas F.
    Hubard, Alfredo
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 368 (05) : 3271 - 3303
  • [5] POINT OF INTERSECTION AND CONVEX SETS IN COMPLETED RIEMANNIAN MANIFOLDS
    KARCHER, H
    [J]. MATHEMATISCHE ANNALEN, 1968, 177 (02) : 105 - &
  • [6] Energy of convex sets, shortest paths, and resistance
    Lovász, L
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2001, 94 (02) : 363 - 382
  • [7] Center of Distances and Central Cantor Sets
    Michał Banakiewicz
    Artur Bartoszewicz
    Małgorzata Filipczak
    Franciszek Prus-Wiśniowski
    [J]. Results in Mathematics, 2022, 77
  • [8] The Center of Distances of Central Cantor Sets
    Banakiewicz, Michal
    [J]. RESULTS IN MATHEMATICS, 2023, 78 (06)
  • [9] Center of Distances and Central Cantor Sets
    Banakiewicz, Michal
    Bartoszewicz, Artur
    Filipczak, Malgorzata
    Prus-Wisniowski, Franciszek
    [J]. RESULTS IN MATHEMATICS, 2022, 77 (05)
  • [10] The Center of Distances of Central Cantor Sets
    Michał Banakiewicz
    [J]. Results in Mathematics, 2023, 78
12345