AN INTERIOR-POINT COLUMN GENERATION METHOD FOR LINEAR-PROGRAMMING USING SHIFTED BARRIERS

被引：8
作者：
MITCHELL, JE
机构：
来源：
SIAM JOURNAL ON OPTIMIZATION | 1994年 / 4卷 / 02期
关键词：
LINEAR PROGRAMMING; COLUMN GENERATION; INTERIOR POINT ALGORITHMS; SHIFTED BARRIERS; POLYNOMIALITY;
D O I：
10.1137/0804023
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A column generation method for linear programming problems is described. This method is based on Freund's shifted barrier method for linear programming. The use of shifts makes it possible to give new primal variables the value zero, with the resulting point being both feasible and interior in the shifted or relaxed formulation. The algorithm takes O(nL) iterations. It is shown that the direction obtained when using the shifted barrier column generation method is related to one proposed by Mitchell and Todd. Preliminary computational results are included, which show that the method may be useful when small numbers of variables are added.
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收藏
页码：423 / 440
页数：18
相关论文
共 18 条
[1]  
ATKINSON DS, 1992, ANAL CTR BASED CUTTI
[2]   YALE SPARSE-MATRIX PACKAGE .1. THE SYMMETRIC CODES [J].
EISENSTAT, SC ;
GURSKY, MC ;
SCHULTZ, MH ;
SHERMAN, AH .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1982, 18 (08) :1145-1151
[3]   A POTENTIAL-FUNCTION REDUCTION ALGORITHM FOR SOLVING A LINEAR PROGRAM DIRECTLY FROM AN INFEASIBLE WARM START [J].
FREUND, RM .
MATHEMATICAL PROGRAMMING, 1991, 52 (03) :441-466
[4]   POLYNOMIAL-TIME ALGORITHMS FOR LINEAR-PROGRAMMING BASED ONLY ON PRIMAL SCALING AND PROJECTED GRADIENTS OF A POTENTIAL FUNCTION [J].
FREUND, RM .
MATHEMATICAL PROGRAMMING, 1991, 51 (02) :203-222
[5]   DECOMPOSITION AND NONDIFFERENTIABLE OPTIMIZATION WITH THE PROJECTIVE ALGORITHM [J].
GOFFIN, JL ;
HAURIE, A ;
VIAL, JP .
MANAGEMENT SCIENCE, 1992, 38 (02) :284-302
[6]   CUTTING PLANES AND COLUMN GENERATION TECHNIQUES WITH THE PROJECTIVE ALGORITHM [J].
GOFFIN, JL ;
VIAL, JP .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1990, 65 (03) :409-429
[7]   PATH-FOLLOWING METHODS FOR LINEAR-PROGRAMMING [J].
GONZAGA, CC .
SIAM REVIEW, 1992, 34 (02) :167-224
[8]   ON LOWER BOUND UPDATES IN PRIMAL POTENTIAL REDUCTION METHODS FOR LINEAR-PROGRAMMING [J].
GONZAGA, CC .
MATHEMATICAL PROGRAMMING, 1991, 52 (03) :415-428
[9]   SOLUTION OF LARGE-SCALE SYMMETRICAL TRAVELING SALESMAN PROBLEMS [J].
GROTSCHEL, M ;
HOLLAND, O .
MATHEMATICAL PROGRAMMING, 1991, 51 (02) :141-202
[10]  
HELGASON RV, 1985, NETFLO COMPUTER PROG
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