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On parametric vector optimization via metric regularity of constraint systems

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Abstract

Some metric and graphical regularity properties of generalized constraint systems are investigated. Then, these properties are applied in order to penalize (in the sense of Clarke) various scalar and vector optimization problems. This method allows us to present several necessary optimality conditions in solid constrained vector optimization.

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References

  • Bao TQ, Gupta P, Mordukhovich BS (2007) Necessary conditions for multiobjective optimization with equilibrium constraints. J Optim Theory Appl 135: 179–203

    Article  MathSciNet  MATH  Google Scholar 

  • Clarke FH (1983) Optimization and nonsmooth analysis. Wiley, New York

    MATH  Google Scholar 

  • Dontchev AL, Rockafellar RT (2009) Implicit functions and solution mappings. Springer, Berlin

    Book  MATH  Google Scholar 

  • Durea M, Strugariu R (2010) Quantitative results on openness of set-valued mappings and implicit multifunction theorems. Pac J Optim 6: 533–549

    MathSciNet  MATH  Google Scholar 

  • Durea M, Strugariu R (2011a) On some Fermat rules for set-valued optimization problems. Optimization 60: 575–591

    Article  MathSciNet  MATH  Google Scholar 

  • Durea M, Strugariu R (2011b) Openness stability and implicit multifunction theorems. Applications to variational systems. Nonlinear Anal Theory Methods. doi:10.1016/j.na.2011.02.019

  • Durea M, Tammer C (2009) Fuzzy necessary optimality conditions for vector optimization problems. Optimization 58: 449–467

    Article  MathSciNet  MATH  Google Scholar 

  • Liu G, Ye J, Zhu J (2008) Partial exact penalty for mathematical programs with equilibrium constraints. Set-Valued Anal 16: 785–804

    Article  MathSciNet  MATH  Google Scholar 

  • Mordukhovich BS (2006) Variational analysis and generalized differentiation, vol I: basic theory, vol II: applications, Springer, Grundlehren der mathematischen Wissenschaften (A series of comprehensive studies in mathematics) vol 330 and 331, Berlin

  • Mordukhovich BS (2009) Multiobjective optimization problems with equilibrium constraints. Math Program 117: 331–354

    Article  MathSciNet  MATH  Google Scholar 

  • Mordukhovich BS, Nam NM (2005) Subgradient of distance functions with applications to Lipschitzian stability. Math Program Ser B 104: 635–668

    Article  MathSciNet  MATH  Google Scholar 

  • Robinson SM (1980) Strongly regular generalized equations. Math Oper Res 5: 43–62

    Article  MathSciNet  MATH  Google Scholar 

  • Rockafellar RT (1985) Lipschitzian properties of multifunctions. Nonlinear Anal Theory Methods Appl 9: 867–885

    Article  MathSciNet  MATH  Google Scholar 

  • Thibault L (1991) On subdifferentials of optimal value functions. SIAM J Control Optim 29: 1019–1036

    Article  MathSciNet  MATH  Google Scholar 

Download references

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Authors and Affiliations

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

    M. Durea

  2. Department of Mathematics, “Gh. Asachi” Technical University, Bd. Carol I, nr. 11, 700506, Iasi, Romania

    R. Strugariu

Authors
  1. M. Durea
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  2. R. Strugariu
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Correspondence to M. Durea.

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Durea, M., Strugariu, R. On parametric vector optimization via metric regularity of constraint systems. Math Meth Oper Res 74, 409–425 (2011). https://doi.org/10.1007/s00186-011-0370-5

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  • DOI: https://doi.org/10.1007/s00186-011-0370-5

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