Interior penalty functions and duality in linear programming

被引：4

作者：

Eremin, I. I. ^{[1
,2
]}

Popov, L. D. ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Inst Math & Mech, Ural Branch, Ekaterinburg 620990, Russia

[2] Ural Fed Univ, Inst Math & Comp Sci, Ekaterinburg 620000, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2013年 / 283卷

基金：

俄罗斯基础研究基金会;

关键词：

linear programming; duality; inner penalty functions;

D O I：

10.1134/S0081543813090058

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Logarithmic additive terms of barrier type with a penalty parameter are included in the Lagrange function of a linear programming problem. As a result, the problem of searching for saddle points of the modified Lagrangian becomes unconstrained (the saddle point is sought with respect to the whole space of primal and dual variables). Theorems on the asymptotic convergence to the desired solution and analogs of the duality theorems for the arising optimization minimax and maximin problems are formulated.

引用

页码：56 / 63

页数：8

共 9 条

[1] Elster K.-H., 1977, EINFUHRUNG NICHTLINE
[2] Eremin I.I., 2002, INVER ILL POSED PROB
[3] Eremin II., 1976, Introduction to the Theory of Linear and Convex Programming
[4] Evtushenko Yu.G., 1982, Methods for Solving Extremal Problems and Their Application in Optimization Systems
[5] Fiacco AV, 1972, NONLINEAR PROGRAMMIN
[6] Roos Cornelis., 1997, Theory and algorithms for linear optimization
[7] Barrier Function Method and Correction Algorithms for Improper Convex Programming Problems
Skarin, V. D.
[J]. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2008, 263 (Suppl 2) : S120 - S134
[8] Vasilev F. P., 1988, Numerical Methods for Solving Extremal Problems
[9] Zangwill W, 1973, Nelineinoe programmirovanie: edinyi podkhod

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