Skip to main content
SpringerLink
Log in

First and second order optimality conditions for set-valued optimization problems

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

In this paper we study first and second order necessary and sufficient optimality conditions for optimization problems involving set-valued maps and we derive some known results in a more general framework.

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. Aleman A,On some generalization of convex sets and convex functions, Mathematica-Revue d’Analyse Numerique et de Théorie de l’Approximation,14 (1985), 1–6.

    MATH  MathSciNet  Google Scholar 

  2. Aubin J.-P., Frankowska H.,Set-valued analysis, Birkhäuser: Basel, Berlin, 1990.

    MATH  Google Scholar 

  3. Bigi G., Castellani M.,K — epiderivatives for set-valued functions and optimization, Mathematical Methods of Operations Research,55 (2002), 401–412.

    Article  MATH  MathSciNet  Google Scholar 

  4. Breckner W. W., Kassay G.,A Systematization of Convexity Concepts for Sets and Functions, Journal of Convex Analysis,4 (1997), 109–127.

    MATH  MathSciNet  Google Scholar 

  5. Corley H. W.,Optimality Conditions for Maximization of Set-Valued Functions, Journal of Optimization Theory and Applications,58 (1988), 1–10.

    Article  MathSciNet  Google Scholar 

  6. Jahn R., Rauh R.,Contingent epiderivatives and set-valued optimization, Mathematical Methods of Operations Research,46 (1997), 193–211.

    Article  MATH  MathSciNet  Google Scholar 

  7. Jimenez B., Novo V.,A notion of local proper efficiency in the Borwein sense in vector optimization, ANZIAM Journal,22 (2003), pp. 75–89.

    Article  MathSciNet  Google Scholar 

  8. Luc D. T.,Theory of Vector Optimization Springer Verlag, Berlin, 1989.

    Google Scholar 

  9. Penot J.-P.,Differentiability of relations and differential stability perturbed optimization problems, SIAM Journal on Control and Optimization,22 (1984), 529–551.

    Article  MATH  MathSciNet  Google Scholar 

  10. Penot J.-P.,Metric estimates for the calculus of multimappings, Set-Valued Analysis,5 (1997), 291–308.

    Article  MATH  MathSciNet  Google Scholar 

  11. Taa A.,Set-valued derivatives of multifunctions and optimality conditions, Numerical Functional Analysis and Optimization,19 (1998), 121–140.

    Article  MATH  MathSciNet  Google Scholar 

  12. Ursescu C.,Tangent sets’ calculus and necessary conditions for extremality, SIAM Journal on Control Optimization,36 (1982), 563–574.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics, “Al. I. Cuza” University, Bd. Carol I, nr. 11, 700506, Iaşi, Romania

    M. Durea

Authors
  1. M. Durea
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Durea, M. First and second order optimality conditions for set-valued optimization problems. Rend. Circ. Mat. Palermo 53, 451–468 (2004). https://doi.org/10.1007/BF02875738

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02875738

Key words

Search

Navigation