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.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
Bao TQ, Gupta P, Mordukhovich BS (2007) Necessary conditions for multiobjective optimization with equilibrium constraints. J Optim Theory Appl 135: 179–203
Clarke FH (1983) Optimization and nonsmooth analysis. Wiley, New York
Dontchev AL, Rockafellar RT (2009) Implicit functions and solution mappings. Springer, Berlin
Durea M, Strugariu R (2010) Quantitative results on openness of set-valued mappings and implicit multifunction theorems. Pac J Optim 6: 533–549
Durea M, Strugariu R (2011a) On some Fermat rules for set-valued optimization problems. Optimization 60: 575–591
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
Liu G, Ye J, Zhu J (2008) Partial exact penalty for mathematical programs with equilibrium constraints. Set-Valued Anal 16: 785–804
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
Mordukhovich BS, Nam NM (2005) Subgradient of distance functions with applications to Lipschitzian stability. Math Program Ser B 104: 635–668
Robinson SM (1980) Strongly regular generalized equations. Math Oper Res 5: 43–62
Rockafellar RT (1985) Lipschitzian properties of multifunctions. Nonlinear Anal Theory Methods Appl 9: 867–885
Thibault L (1991) On subdifferentials of optimal value functions. SIAM J Control Optim 29: 1019–1036
About this article
Cite this article
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