An infinite-dimensional LP duality theorem

被引：6

作者：

Clark, SA ^{[1
]}

机构：

[1] Univ Kentucky, Dept Stat, Lexington, KY 40506 USA

来源：

MATHEMATICS OF OPERATIONS RESEARCH | 2003年 / 28卷 / 02期

关键词：

linear program; strictly positive; adjoint operator; algebraic dual; topological dual;

D O I：

10.1287/moor.28.2.233.14479

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

This paper constructs an infinite-dimensional version of the Duality Theorem for a Linear Program (LP). The algebraic dual LP is replaced with a new program called the topological dual LP that closes the range of the adjoint operator. Under some mild nondegeneracy conditions involving strict positivity, the new Duality Theorem asserts that the optimal value of the primal LP equals the optimal value of the topological dual LP. Some applications to mathematical finance are also included.

引用

页码：233 / 245

页数：13

共 50 条

[1] AN INFINITE-DIMENSIONAL SCHOENFLIES THEOREM
SANDERSON, DE
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 148 (01) : 33 - +
[2] INFINITE-DIMENSIONAL ANALOG OF ZIGEL THEOREM
NOVIKOVA, LV
[J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1982, 16 (02) : 141 - 143
[3] An infinite-dimensional generalization of the Jung theorem
V. Nguen-Khac
K. Nguen-Van
[J]. Mathematical Notes, 2006, 80 : 224 - 232
[4] An infinite-dimensional generalization of the jung theorem
Nguen-Khac, V.
Nguen-Van, K.
[J]. MATHEMATICAL NOTES, 2006, 80 (1-2) : 224 - 232
[5] An infinite-dimensional linking theorem and applications
Schechter, M
Zou, WM
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 201 (02) : 324 - 350
[6] INFINITE-DIMENSIONAL EXTENSION OF A THEOREM OF KOMLOS
BALDER, EJ
[J]. PROBABILITY THEORY AND RELATED FIELDS, 1989, 81 (02) : 185 - 188
[7] ZERO DUALITY GAPS IN INFINITE-DIMENSIONAL PROGRAMMING
JEYAKUMAR, V
WOLKOWICZ, H
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1990, 67 (01) : 87 - 108
[8] On the Metric Compactification of Infinite-dimensional lp Spaces
Gutierrez, Armando W.
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2019, 62 (03): : 491 - 507
[9] AN EXTENSION OF BURNSIDE THEOREM TO INFINITE-DIMENSIONAL SPACES
LOMONOSOV, V
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1991, 75 (2-3) : 329 - 339
[10] A fixed point theorem for the infinite-dimensional simplex
Rizzolo, Douglas
Su, Francis Edward
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 332 (02) : 1063 - 1070

← 1 2 3 4 5 →