Abstract
In this paper we use the penalty approach in order to study a class of constrained minimization problems on complete metric spaces. A penalty function is said to have the generalized exact penalty property if there is a penalty coefficient for which approximate solutions of the unconstrained penalized problem are close enough to approximate solutions of the corresponding constrained problem. For our class of problems we establish the generalized exact penalty property and obtain an estimation of the exact penalty.
Similar content being viewed by others
References
Boukari D., Fiacco A.V.: Survey of penalty, exact-penalty and multiplier methods from 1968 to 1993. Optimization 32, 301–334 (1995)
Clarke F.H.: Optimization and nonsmooth analysis. Wiley, New York (1983)
Demyanov V.F.: Extremum conditions and variational problems. St. Peterb. Gos. Univ., St. Petersburg (2000)
Demyanov V.F.: Exact penalty functions and problems of the calculus of variations. Avtomat. i Telemekh. 2, 136–147 (2004)
Demyanov V.F., Di Pillo G., Facchinei F.: Exact penalization via Dini and Hadamard conditional derivatives. Optim. Methods Softw. 9, 19–36 (1998)
Di Pillo G., Grippo L.: Exact penalty functions in constrained optimization. SIAM J. Control Optim. 27, 1333–1360 (1989)
Ekeland I.: On the variational principle. J. Math. Anal. Appl. 47, 324–353 (1974)
Eremin I.I.: The penalty method in convex programming. Sov. Math. Dokl. 8, 459–462 (1966)
Mordukhovich B.S.: Variational analysis and generalized differentiation, II: applications. Springer, Berlin (2006)
Zangwill W.I.: Nonlinear programming via penalty functions. Manag. Sci. 13, 344–358 (1967)
Zaslavski A.J.: A sufficient condition for exact penalty in constrained optimization. SIAM J. Optim. 16, 250–262 (2005)
Zaslavski A.J.: Existence of approximate exact penalty in constrained optimization. Math. Oper. Res. 32, 484–495 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zaslavski, A.J. An exact penalty approach to constrained minimization problems on metric spaces. Optim Lett 7, 1009–1016 (2013). https://doi.org/10.1007/s11590-012-0500-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11590-012-0500-x
Keywords
- Approximate solution
- Complete metric space
- Ekeland’s variational principle
- Minimization problem
- Penalty function