Farkas’ Lemma, Gale’s Theorem, and Linear Programming: the Infinite Case in an Algebraic Way
Abstract
Full Text:
PDFReferences
E. J. Anderson and P. Nash, Linear Programming in Infinite-Dimensional Spaces, Wiley, Chichester, 1987.
D. Bartl, Farkas’ Lemma, other theorems of the alternative, and linear programming in infinite-dimensional spaces:
a purely linear-algebraic approach, Linear and Multilinear Algebra, 55 (2007) 327–353.
D. Bartl, A Short Algebraic Proof of the Farkas Lemma, SIAM Journal on Optimization, 19 (2008) 234–239.
D. Bartl, A note on the short algebraic proof of Farkas’ Lemma, Linear and Multilinear Algebra, 60 (2012) 897–901.
D. Bartl, A very short algebraic proof of the Farkas Lemma, Mathematical Methods of Operations Research, 75
(2012) 101–104.
D. Bartl, Separation theorems for convex polytopes and finitely-generated cones derived from theorems of the alternative,
Linear Algebra and its Applications, 436 (2012) 3784–3789.
P. M. Cohn, Skew fields: Theory of general division rings, Cambridge University Press, 1995.
K. Fan, On Systems of Linear Inequalities. In: H.W. Kuhn and A.W. Tucker (eds.), Linear Inequalities and Related
Systems, Princeton University Press, Princeton, 1956, 99–156.
J. Farkas, Theorie der einfachen Ungleichungen, Journal f¨ur die reine und angewandte Mathematik, 124 (1902)
–27.
D. Gale, The Theory of Linear Economic Models, McGraw-Hill, New York, 1960.
D. Gale, H. W. Kuhn, and A. W. Tucker, Linear Programming and the Theory of Games. In: T. C. Koopmans (ed.),
Activity Analysis of Production and Allocation, Wiley, New York, 1951, 317–329.
M. A. Goberna and M. A. L´opez, Linear Semi-Infinite Optimization, Wiley, Chichester, 1998.
T. Y. Lam, A First Course in Noncommutative Rings, Springer, New York, Berlin, 1991.
Refbacks
- There are currently no refbacks.