Skip to main content
SpringerLink
Log in

Constructive Generalization of Classical Sufficient Second-Order Optimality Conditions

  • MATHEMATICS
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

New sufficient second-order optimality conditions for equality constrained optimization problems are proposed, which significantly strengthen and complement classical ones and are constructive. For example, they establish the equivalence between sufficient conditions for inequality constrained optimization problems and sufficient conditions for optimality in equality constrained problems by reducing the former to equalities via introducing slack variables. Previously, in the case of classical sufficient optimality conditions, this fact was not considered to be true, that is, the existing classical sufficient conditions were not complete. Accordingly, the proposed optimality conditions complement the classical ones and solve the issue of equivalence between inequality and equality constrained problems when the former is reduced to the latter by introducing slack variables.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. Yu. G. Evtushenko, Methods for Solving Optimization Problems and Their Applications in Optimization Systems (Nauka, Moscow, 1982) [in Russian].

    MATH  Google Scholar 

  2. B. T. Polyak, Introduction to Optimization (Nauka, Moscow, 1983; Optimization Software, New York, 1987).

  3. O. A. Brezhneva, Yu. G. Evtushenko, and A. A. Tret’yakov, Dokl. Math. 73 (3), 384–387 (2006).

    Article  Google Scholar 

  4. D. P. Bertsekas, Nonlinear Programming (Athena Scientific, Belmont, Mass. 1999), pp. 191–276.

    MATH  Google Scholar 

  5. O. A. Brezhneva and A. A. Tret’yakov, Numer. Funct. Anal. Optim. 28 (9–10), 1051–1086 (2007).

    Article  MathSciNet  Google Scholar 

Download references

Funding

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

Author information

Authors and Affiliations

  1. Dorodnitsyn Computing Center, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333, Moscow, Russia

    Yu. G. Evtushenko & A. A. Tret’yakov

  2. Moscow Institute of Physics and Technology (State University), 141700, Dolgoprudnyi, Moscow oblast, Russia

    Yu. G. Evtushenko

  3. Moscow Aviation Institute (National Research University), 125080, Moscow, Russia

    Yu. G. Evtushenko

  4. System Research Institute, Polish Academy of Sciences, 01-447, Warsaw, Poland

    A. A. Tret’yakov

  5. Siedlce University, 08-110, Siedlce, Poland

    A. A. Tret’yakov

Authors
  1. Yu. G. Evtushenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Tret’yakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yu. G. Evtushenko or A. A. Tret’yakov.

Additional information

Translated by I. Ruzanova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Evtushenko, Y.G., Tret’yakov, A.A. Constructive Generalization of Classical Sufficient Second-Order Optimality Conditions. Dokl. Math. 100, 372–373 (2019). https://doi.org/10.1134/S106456241904015X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S106456241904015X

Search

Navigation