A multivalued approach to the Farkas lemma

1979 ◽  
pp. 42-47 ◽  
Author(s):  
J. M. Borwein
Keyword(s):  
Farkas Lemma

scholarly journals The Farkas lemma of Shimizu, Aiyoshi and Katayama

1985 ◽  
Vol 31 (3) ◽  
pp. 445-450 ◽  
Author(s):  
Charles Swartz
Keyword(s):  
Convex Programming ◽  
Infinite Dimensional ◽  
Farkas Lemma ◽  
Finite Dimensional

Shimizu, Aiyoshi and Katayama have recently given a finite dimensional generalization of the classical Farkas Lemma. In this note we show that a result of Pshenichnyi on convex programming can be used to give a generalization of the result of Shimizu, Aiyoshi and Katayama to infinite dimensional spaces. A generalized Farkas Lemma of Glover is also obtained.

A Simple Proof of Farkas' Lemma

1998 ◽  
Vol 105 (10) ◽  
pp. 949 ◽  
Author(s):  
Vilmos Komornik
Keyword(s):  
Simple Proof ◽  
Farkas Lemma

Integer Farkas Lemma

2015 ◽  
Vol 17 (01) ◽  
pp. 1540003 ◽  
Author(s):  
R. Chandrasekaran
Keyword(s):  
Nonnegative Integer ◽  
Original System ◽  
Single Equation ◽  
Integer Solution ◽  
Polynomial Algorithms ◽  
Inequality System ◽  
Farkas Lemma ◽  
Single Constraint ◽  
Nonnegative Solutions ◽  
Integer Solutions

Farkas type results are available for solutions to linear systems. These can also include restrictions such as nonnegative solutions or integer solutions. They show that the unsolvability can be reduced to a single constraint that is not solvable and this condition is implied by the original system. Such a result does not exist for integer solution to inequality system because a single inequality is always solvable in integers. But a single equation that does not have nonnegative integer solution exists. We present some cases when polynomial algorithms to find nonnegative integer solutions exist.

scholarly journals A new version of Farkas' lemma and global convex maximization

1993 ◽  
Vol 6 (5) ◽  
pp. 39-43 ◽  
Author(s):  
V. Jeyakumar ◽  
B.M. Glover
Keyword(s):  
Convex Maximization ◽  
Farkas Lemma
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