The p-Factor Method for Nonlinear Optimization

• Autorzy: Szczepanik E.. , Prusińska A. , Tret’yakov A.
• Języki publikacji: EN

Abstrakty

EN

We present the main concept and results of the p-regularity theory (also known as p-factor analysis of nonlinear mappings) applied to nonlinear optimization problems. The approach is based on the construction of p-factor operator. The main result of this theory gives a detailed description of the structure of the zero set of irregular nonlinear mappings. Applications include a new numerical method for solving nonlinear optimization problems and p- order necessary and sufficient optimality conditions. We substantiate the rate of convergence of p-factor method.

Słowa kluczowe

EN

nonlinear optimization; p-factor operator; p-regularity; kernel; singularity; convergence; necessary and sufficient conditions

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Schedae Informaticae
• Rocznik: 2012
• Tom: Vol. 21
• Strony: 141--157
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Szczepanik E..

• Siedlce University of Natural Sciences and Humanities, Siedlce, Poland

autor

Prusińska A.

• Siedlce University of Natural Sciences and Humanities, Siedlce, Poland

autor

Tret’yakov A.

• Siedlce University of Natural Sciences and Humanities, Siedlce, Poland
• System Research Institute of the Polish Academy of Sciences, Warsaw, Poland, Dorodnicyn Computing Center of the Russian Academy of Sciences, Moscow, Russia

Bibliografia

• [1] Brezhneva O.A., Tret’yakov A.A.; Optimality conditions for degenerate extremum problems with equality constraints, SIAM J. Contr. Optim. 12, 2003, pp. 729–745.
• [2] Belash K.N., Tret’yakov A.A.; Methods for solving degenerate problems, USSR Comput. Math. and Math. Phys. 28, 1988, pp. 90–94.
• [3] Korneva I.T., Tret’yakov A.A.; Application of the factor-analysis to the calculus of variations, Proceedings of Simulation and Analysis in Problems of Decision-Making Theory, Computing Center of Russian Academy of Sciences, Moscow, 2002, pp. 144–162 (in Russian).
• [4] Prusińska A., Tret’yakov A.A.; P-order Necessary and Sufficient Conditions for Optimality in Singular Calculus of Variations, Discussiones Mathematicae, Differential Inclusions, Control and Optimization 30, 2010, pp. 269–279.
• [5] Szczepanik E., Tret’yakov A.A.; Methods for irregular equality-constrained optimization problems, Nonlinear Analysis 69, 2008, pp. 4241–4251.
• [6] Tret’yakov A.A., Marsden J.E.; Factor analysis of nonlinear Mappings: p-regularity theory, Computations on Pure and Applied Analysis 2(4), 2003, pp. 425–445.
• [7] Tret’yakov A.A.; Necessary and sufficient conditions for optimality of p-th order, Comput. Math. and Math. Phys. 24, 1984, pp. 123–127.
• [8] Tret’yakov A.A.; The implicit function theorem in degenerate problems, Russ. Math. Surv. 42, 1987, pp. 179–180.
• [9] Polyak B.T.; Introduction to optimization, Nauka, Moscow 1983 (in Russian).
• [10] Brezhneva O.A., Tret’yakov A.A.; New methods for solving nonlinear problems, Computing Center of the Russian Academy of Sciences, Moscow 2000 (in Russian).