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P-Regularity Theory: Applications to Optimization

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Optimization and Applications (OPTIMA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12422))

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Abstract

We present recent advances in the analysis of nonlinear structures and their applications to nonlinear optimization problems with constraints given by nonregular mappings or other singularities obtained within the framework of the p-regularity theory developed over the last twenty years. In particular, we address the problem of description of the tangent cone to the solution set of the operator equation, optimality conditions, and solution methods for optimization problems.

This work was supported in part by the Russian Foundation for Basic Research, project No. 17-07-00510.

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References

  1. Ashmanov, S.A., Timokhov, A.V.: Optimization Theory in Tasks and Exercises (in Russian). Fizmatlit, Moscow (1991)

    Google Scholar 

  2. Belash, K.N., Tret’yakov, A.A.: Methods for solving degenerate problems. USSR Comput. Math. Math. Phys. 28(4), 90–94 (1988)

    Article  MathSciNet  Google Scholar 

  3. Bertsekas, D.P.: Nonlinear Programming. Athena Scientific, Belmont (1999)

    MATH  Google Scholar 

  4. Brezhneva, O.A., Tret’yakov, A.A.: The p-factor-Lagrange methods for degenerate nonlinear programming. Numer. Funct. Anal. Optim. 28(9–10), 1051–1086 (2007)

    Article  MathSciNet  Google Scholar 

  5. Evtushenko, Y.G., Tretyakov, A.A.: pth-order approximation of the solution set of nonlinear equations. Comput. Math. Math. Phys. 53(12), 1763–1780 (2013)

    Article  MathSciNet  Google Scholar 

  6. Evtushenko, Y.G.: Methods for Solving Extreme Problems and Their Application in Optimization Systems (in Russian). Nauka, Moscow (1982)

    Google Scholar 

  7. Ioffe, A.D., Tihomirov, V.M.: Theory of Extremal Problems. North-Holland, New York (1979)

    MATH  Google Scholar 

  8. Kuhn, H.W., Tucker, A.W.: Nonlinear programming. In: Proceedings of 2nd Berkeley Symposium, pp. 481–492. University of California Press, Berkeley (1951)

    Google Scholar 

  9. Polyak, B.T.: Introduction to Optimization (in Russian). Nauka, Moscow (1983)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dorodnicyn Computing Centre, FRC CSC RAS, Vavilov Street 40, 119333, Moscow, Russia

    Yuri Evtushenko, Vlasta Malkova & Alexey Tret’yakov

  2. Moscow Institute of Physics and Technology, Moscow, Russia

    Yuri Evtushenko

  3. Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Alexey Tret’yakov

  4. Faculty of Sciences, Siedlce University, 08-110, Siedlce, Poland

    Alexey Tret’yakov

Authors
  1. Yuri Evtushenko
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  2. Vlasta Malkova
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  3. Alexey Tret’yakov
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Corresponding author

Correspondence to Vlasta Malkova .

Editor information

Editors and Affiliations

  1. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  4. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Evtushenko, Y., Malkova, V., Tret’yakov, A. (2020). P-Regularity Theory: Applications to Optimization. In: Olenev, N., Evtushenko, Y., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2020. Lecture Notes in Computer Science(), vol 12422. Springer, Cham. https://doi.org/10.1007/978-3-030-62867-3_8

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