Nonstandard models and optimization
Автор: Kutateladze Semen Samsonovich
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 4 т.10, 2008 года.
Бесплатный доступ
This is an overview of a few possibilities that are open by model theory in optimization. Most attention is paid to the impact of infinitesimal analysis and Boolean valued models to convexity, Pareto optimality, and hyperapproximation.
Boolean valued analysis, nonstandard analysis, approximate efficiency, hyperapproximation, lattice normed space
Короткий адрес: https://sciup.org/14318258
IDR: 14318258
Список литературы Nonstandard models and optimization
- Kantorovich L. V. Functional Analysis and Applied Mathematics//Vestnik Leningrad Univ. Math.-1948.-Vol. 6.-P. 3-18.
- Kantorovich L. V. Functional Analysis and Applied Mathematics//Uspekhi Mat. Nauk.-1948.-Vol. 3, №6.-P. 3-50.
- Kantorovich L. V. On Semiordered Linear Spaces and Their Applications in the Theory of Linear Operators//Dokl. Akad. Nauk SSSR.-1935.-Vol. 4, №1/2.-P. 11-14.
- Kantorovich L. V. The Principle of Majorants and the Newton Method//Dokl. Akad. Nauk SSSR.-1951.-Vol. 76, №1.-P.17-20.
- Sobolev S. L., Lyusternik L. A., Kantorovich L. V. Functional Analysis and Computational Mathematics//Proceedings of the Third All-Union Mathematical Congress, Moscow, June-July.-Moscow, 1956.-Vol. 2.-P. 43.
- Kantorovich L. V. Functional Analysis (the Main Ideas)//Sibirsk. Mat. Zh.-1987.-Vol. 28, № 1.-P.7-16.
- Kantorovich L. V. My Way in Science//Uspekhi Mat. Nauk.-1987.-Vol. 48, №2.-P. 183-213.
- Kantorovich L. V. Selected Works. Part I. Descriptive Theory of Sets and Functions. Functional Analysis in Semi-ordered Spaces.-Amsterdam: Gordon and Breach Publishers, 1996.
- Kantorovich L. V. Selected Works. Part II. Applied Functional Analysis. Approximation Methods and Computers.-Amsterdam: Gordon and Breach Publishers, 1996.
- Kusraev A. G. Dominated Operators.-Dordrecht: Kluwer Academic Publishers, 2001; Moscow: Nauka, 2003.
- Kusraev A. G., Kutateladze S. S. Introduction to Boolean Valued Analysis.-Moscow: Nauka, 2005.
- Kutateladze S. S. Convex Operators//Uspekhi Mat. Nauk.-1979.-Vol. 34, №1.-P. 167-196.
- Kutateladze S. S. Convex $\varepsilon$-Programming//Dokl. Akad. Nauk SSSR.-1979.-Vol. 245, №5.-P. 1048-1050.
- Kutateladze S. S. A Version of Nonstandard Convex Programming//Sibirsk. Mat. Zh.-1986.-Vol. 27, №4.-P. 84-92.
- Kusraev A. G., Kutateladze S. S. Subdifferential Calculus: Theory and Applications.-Moscow: Nauka, 2007.
- Gordon E. I., Kusraev A. G., Kutateladze S. S. Infinitesimal Analysis: Selected Topics.-Moscow: Nauka, 2008.
- Zalinescu C. Convex Analysis in General Vector Spaces.-London: World Scientific Publishers, 2002.
- Singer I. Abstract Convex Analysis.-New York: John Wiley & Sons, 1997.
- Gutierrez C., Jimenez B., Novo V. On Approximate Solutions in Vector Optimization Problems via Scalarization//Comput. Optim. Appl.-2006.-Vol. 35, №3.-P. 305-324.
- Gutierrez C., Jimenez B., Novo V. Optimality Conditions for Metrically Consistent Approximate Solutions in Vector Optimization//J. Optim. Theory Appl.-2007.-Vol. 133, № 1.-P. 49-64.
Статья научная
