Linear-programming approach to nonconvex variational problems

被引：7
|
作者：
Bartels, S [1 ]
Roubícek, T
机构：
[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA
[2] Charles Univ, Math Inst, Prague 18675 8, Czech Republic
[3] Acad Sci Czech Republ, Inst Informat Theory & Automat, CR-18208 Prague 8, Czech Republic
来源：
NUMERISCHE MATHEMATIK | 2004年 / 99卷 / 02期
关键词：
D O I：
10.1007/s00211-004-0549-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In nonconvex optimization problems, in particular in nonconvex variational problems, there usually does not exist any classical solution but only generalized solutions which involve Young measures. In this paper, after reviewing briefly the relaxation theory for such problems, an iterative scheme leading to a "sequential linear programming" (= SLP) scheme is introduced, and its convergence is proved by a Banach fixed-point technique. Then an approximation scheme is proposed and analyzed, and calculations of an illustrative 2D "broken-extremal" example are presented.
引用
收藏
页码：251 / 287
页数：37
相关论文
共 50 条
  • [1] Linear-programming approach to nonconvex variational problems
    Sören Bartels
    Tomáš Roubíček
    [J]. Numerische Mathematik, 2004, 99 : 251 - 287
  • [2] AN APPROACH TO THE ANALYSIS OF IMPROPER PROBLEMS OF LINEAR-PROGRAMMING
    SKARIN, VD
    [J]. USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1986, 26 (02): : 73 - 79
  • [3] Linear decomposition approach for a class of nonconvex programming problems
    Shen, Peiping
    Wang, Chunfeng
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,
  • [4] Linear decomposition approach for a class of nonconvex programming problems
    Peiping Shen
    Chunfeng Wang
    [J]. Journal of Inequalities and Applications, 2017
  • [5] A LINEAR-PROGRAMMING APPROACH TO SOLVING INFEASIBLE RAS PROBLEMS
    MOHR, M
    CROWN, WH
    POLENSKE, KR
    [J]. JOURNAL OF REGIONAL SCIENCE, 1987, 27 (04) : 587 - 603
  • [6] A NEW APPROACH TO SOME POSSIBILISTIC LINEAR-PROGRAMMING PROBLEMS
    LAI, YJ
    HWANG, CL
    [J]. FUZZY SETS AND SYSTEMS, 1992, 49 (02) : 121 - 133
  • [7] DECOMPOSITION OF LINEAR-PROGRAMMING PROBLEMS
    HLAVACEK, J
    [J]. POLITICKA EKONOMIE, 1977, 25 (05) : 443 - 456
  • [8] MIXING PROBLEMS - LINEAR-PROGRAMMING
    SZATMARI, G
    [J]. MAGYAR KEMIKUSOK LAPJA, 1973, 28 (09): : 451 - 457
  • [9] LINEAR-PROGRAMMING CUTTING PROBLEMS
    MUKHACHIOVA, EA
    ZALGALLER, VA
    [J]. INTERNATIONAL JOURNAL OF SOFTWARE ENGINEERING AND KNOWLEDGE ENGINEERING, 1993, 3 (04) : 463 - 476
  • [10] DEGENERACY IN LINEAR-PROGRAMMING PROBLEMS
    ECKHARDT, U
    [J]. ANGEWANDTE INFORMATIK, 1976, (06): : 255 - 258
12345