Convex relaxations for quadratic distance problems

被引：1
|
作者：
Garulli, Andrea [1 ]
Masi, Alfio [1 ]
Vicino, Antonio [1 ]
机构：
[1] Univ Siena, Dipartimento Ingn Informaz, I-53100 Siena, Italy
来源：
47TH IEEE CONFERENCE ON DECISION AND CONTROL, 2008 (CDC 2008) | 2008年
关键词：
POSITIVE POLYNOMIALS; GLOBAL OPTIMIZATION; SQUARES;
D O I：
10.1109/CDC.2008.4739051
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Convex relaxations of nonconvex problems are a powerful tool for the analysis and design of control systems. An important family of nonconvex problems that are relevant to the control field is that of quadratic distance problems. In this paper, several convex relaxations are presented for quadratic distance problems which are based on the sum-of squares representation of positive polynomials. Relationships among the considered relaxations are discussed and numerical comparisons are presented, in order to highlight their degree of conservatism.
引用
收藏
页码：5444 / 5449
页数：6
相关论文
共 50 条
  • [1] Equivalence of sum of squares convex relaxations for quadratic distance problems
    Garulli, Andrea
    Masi, Alfio
    Vicino, Antonio
    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2013, 23 (09) : 965 - 977
  • [2] Solving quadratic assignment problems using convex quadratic programming relaxations
    Brixius, NW
    Anstreicher, KM
    OPTIMIZATION METHODS & SOFTWARE, 2001, 16 (1-4): : 49 - 68
  • [3] Convex quadratic programming relaxations for network scheduling problems
    Skutella, M
    ALGORITHMS - ESA'99, 1999, 1643 : 127 - 138
  • [4] Global solution of quadratic problems using interval methods and convex relaxations
    Elloumi, Sourour
    Lambert, Amelie
    Neveu, Bertrand
    Trombettoni, Gilles
    JOURNAL OF GLOBAL OPTIMIZATION, 2025, 91 (02) : 331 - 353
  • [5] PROBLEMS OF DISTANCE GEOMETRY AND CONVEX PROPERTIES OF QUADRATIC MAPS
    BARVINOK, AI
    DISCRETE & COMPUTATIONAL GEOMETRY, 1995, 13 (02) : 189 - 202
  • [6] DS*: Tighter Lifting-Free Convex Relaxations for Quadratic Matching Problems
    Bernard, Florian
    Theobalt, Christian
    Moeller, Michael
    2018 IEEE/CVF CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR), 2018, : 4310 - 4319
  • [7] On Tractable Convex Relaxations of Standard Quadratic Optimization Problems under Sparsity Constraints
    Bomze, Immanuel
    Peng, Bo
    Qiu, Yuzhou
    Yildirim, E. Alper
    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2025, 204 (03)
  • [8] Convex quadratic relaxations of nonconvex quadratically constrained quadratic programs
    Mitchell, John E.
    Pang, Jong-Shi
    Yu, Bin
    OPTIMIZATION METHODS & SOFTWARE, 2014, 29 (01): : 120 - 136
  • [9] CONVEX RELAXATIONS FOR PERMUTATION PROBLEMS
    Fogel, F.
    Jenatton, R.
    Bach, F.
    D'Aspremont, A.
    SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2015, 36 (04) : 1465 - 1488
  • [10] On convex relaxations for quadratically constrained quadratic programming
    Anstreicher, Kurt M.
    MATHEMATICAL PROGRAMMING, 2012, 136 (02) : 233 - 251
12345