Boolean models and simultaneous inequalities
Author: Kutateladze Semen Samsonovich
Journal: Владикавказский математический журнал @vmj-ru
Article in issue: 3 т.11, 2009.
Free access
Boolean valued analysis is applied to deriving operator versions of the classical Farkas Lemma in the theory of simultaneous linear inequalities.
Farkas lemma, theorem of the alternative, interval equations
Short address: https://sciup.org/14318280
IDR: 14318280 | UDC: 517.983.27:517.972.8
Булевозначные модели и система неравенств
В данной работе применен булевозначный нормативный анализ для получения операторных версий классической леммы Фаркаша в теории систем линейных неравенств.
References Boolean models and simultaneous inequalities
- Floudas C. A., Pardalos P. M. (eds.) Encyclopedia of Optimization.-Berlin etc.: Springer, 2009.-4626 p.
- Kusraev A. G., Kutateladze S. S. Introduction to Boolean Valued Analysis.-Moscow: Nauka, 2005.-526 p.
- Kusraev A. G., Kutateladze S. S. Subdifferential Calculus: Theory and Applications.-Moscow: Nauka, 2007.-560 p.
- Scott D. Boolean Models and Nonstandard Analysis//In: Luxemburg W. (ed.) Applications of Model Theory to Algebra, Analysis, and Probability.-N. Y.: Holt, Rinehart, and Winston, 1969.-P. 87-92.
- Takeuti G. Two Applications of Logic to Mathematics.-Tokyo; Princeton: Iwanami and Princeton Univ. Press, 1978.-137 p.
- Fiedler M. (eds.) Linear Optimization Problems with Inexact Data.-N. Y.: Springer, 2006.-214 p.
- Mangasarian O. L. Set containment characterization//J. Glob. Optim.-2002.-Vol. 24, № 4.-P. 473-480.