Abstract
By means of the Image Space Analysis, duality properties of a constrained extremum problem are investigated. The analysis of the lower semicontinuity of the perturbation function, related to a right-hand side perturbation of the given problem, leads to a characterization of zero duality gap in the image space.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Castellani, M., Mastroeni, G., Pappalardo, M.: In: Di Pillo, G., Giannessi, F. (eds.) On Regularity for Generalized Systems and Applications, Nonlinear Optimization and Applications, pp. 13–26. Plenum Publishing Corporation (1996)
Ekeland I., Temam R.: Analyse Convexe et Problemes Variationnels. Dunod-Gauthier-Villars, Paris (1974)
Frenk J.B.G., Kassay G.: Lagrangian duality and cone convexlike functions. J. Optim. Theory Appl. 134, 207–222 (2007)
Giannessi F., Mastroeni G.: Separation of sets and Wolfe duality. J. Glob. Optim. 42, 401–412 (2008)
Giannessi F., Rapcsák T.: Images, separation of sets and extremum problems, recent trends in optimization theory and applications. World Sci. Ser. Appl. Anal. 5, 79–106 (1995)
Giannessi, F.: Constrained Optimization and Image Space Analysis. Springer, London (2005)
Giannessi F.: Theorems of the alternative and optimality conditions. J. Optim. Theory Appl. 42, 331–365 (1984)
Giannessi F.: Semidifferentiable functions and necessary optimality conditions. J. Optim. Theory Appl. 60, 191–241 (1989)
Giannessi, F., Mastroeni, G., Pellegrini, L.: On the theory of vector optimization and variational inequalities image space analysis and separation. In: Giannessi, F. (ed.) Vector Variational Inequalities and Vector Equilibria. Mathematical Theories, pp. 153–215. Kluwer, Dordrecht (2000)
Jeyakumar V., Wolkowicz H.: Zero duality gaps in infinite-dimensional programming. J. Optim. Theory Appl. 67, 87–108 (1990)
Mastroeni G., Pappalardo M., Yen N.D.: Image of a parametric optimization problem and continuity of the perturbation function. J. Optim. Theory Appl. 81, 193–202 (1994)
Mastroeni G., Rapcsák T.: On convex generalized systems. J. Optim. Theory Appl. 104, 605–627 (2000)
Pappalardo M.: Image space approach to penalty methods. J. Optim. Theory Appl. 64, 141–152 (1990)
Rockafellar, R.T.: Conjugate Duality and Optimization, SIAM (1974)
Rockafellar R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
Tardella F.: On the image of a constrained extremum problem and some applications to the existence of a minimum. J. Optim. Theory Appl. 60, 93–104 (1989)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mastroeni, G. Some applications of the image space analysis to the duality theory for constrained extremum problems. J Glob Optim 46, 603–614 (2010). https://doi.org/10.1007/s10898-009-9445-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-009-9445-8