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2007 | 27 | 1 | 151-164
Tytuł artykułu

On existence of solutions to degenerate nonlinear optimization problems

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EN
Abstrakty
EN
We investigate the existence of the solution to the following problem
min φ(x) subject to G(x)=0,
where φ: X → ℝ, G: X → Y and X,Y are Banach spaces. The question of existence is considered in a neighborhood of such point x₀ that the Hessian of the Lagrange function is degenerate. There was obtained an approximation for the distance of solution x* to the initial point x₀.
Twórcy
  • Institute of Mathematics and Physics, University of Podlasie, 3-go Maja 54, 08-110 Siedlce, Poland
  • Institute of Mathematics and Physics, University of Podlasie, 3-go Maja 54, 08-110 Siedlce, Poland
  • System Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland
Bibliografia
  • [0] V.M. Alexeev, V.M. Tihomirov and S.V. Fomin, Optimal Control, Consultants Bureau, New York, 1987. Translated from Russian by V.M. Volosov.
  • [1] B.P. Demidovitch and I.A. Maron, Basis of Computational Mathematics, Nauka, Moscow 1973. (in Russian)
  • [I-T] A.D. Ioffe and V.M. Tihomirov, Theory of extremal problems, North-Holland, Studies in Mathematics and its Applications, Amsterdam 1979.
  • [4] A.F. Izmailov and A.A. Tret`yakov, Factor-Analysis of Non-Linear Mapping, Nauka, Moscow, Fizmatlit Publishing Company, 1994.
  • [5] L.V. Kantorovitch and G.P. Akilov, Functional Analysis, Pergamon Press, Oxford 1982.
  • [6] M.A. Krasnosel'skii, G.M. Wainikko, P.P. Zabreiko, Yu.B. Rutitskii and V.~Yu. Stetsenko, Approximate Solution of Operator Equations, Wolters-Noordhoff Publishing, Groningen (1972), 39.
  • [M] K. Maurin, Analysis, Part I, Elements, PWN, Warsow 1971. (in Polish)
  • [A-T] A. Prusińska and A.A. Tret'yakov, The theorem on existence of singular solutions to nonlinear equations, Trudy PGU, seria Mathematica, 12 (2005).
  • [9] A.A. Tret'yakov, Necessary Conditions for Optimality of p-th Order, Control and Optimization, Moscow MSU (1983), 28-35 (in Russian).
  • [11] A.A. Tret'yakov, Necessary and Sufficient Conditions for Optimality of p-th Order, USSR Comput. Math. and Math Phys. 24 (1984), 123-127.
  • [8] A.A. Tret'yakov, The implicit function theorem in degenerate problems, Russ. Math. Surv. 42 (1987), 179-180.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1081
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