Abstract
The concept of coercivity is extended to the image space, and it is exploited to obtain a lower bound for the minimum of a constrained extremum problem and a sufficient condition for the optimality. Problems which are coercive in the image space turn out to have zero duality gap. A possible application to variational inequalities is illustrated by means of an example.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cambini, A.,Nonlinear Separation Theorems, Duality, and Optimality Conditions, Optimization and Related Fields, Edited by R. Conti, E. De Giorgi, and F. Giannessi, Springer Verlag, Berlin, Germany, pp. 57–93, 1986.
Giannessi, F.,Theorems of the Alternative, Quadratic Programs, and Complementarity Problems, Variational Inequalities and Complementarity Problems: Theory and Applications, Edited by R. W. Cottle, F. Giannessi, and J. L. Lions, John Wiley, New York, New York, pp. 151–186, 1980.
Giannessi, F.,Theorems of the Alternative and Optimality Conditions, Journal of Optimization Theory and Applications, Vol. 42, pp. 331–365, 1984.
Hestenes, M. R.,Optimization Theory: The Finite-Dimensional Case, John Wiley, New York, New York, 1975.
Tardella, F.,On the Image of a Constrained Extremum Problem and Some Applications to the Existence of the Minimum, Journal of Optimization Theory and Applications, Vol. 60, pp. 93–104, 1989.
Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill, New York, New York, 1969.
Pellegrini, L.,On a Lagrangian Sufficient Optimality Condition, Journal of Optimization Theory and Applications, Vol. 68, pp. 19–33, 1991.
Pellegrini, L.,On Strictly Convex Minorant Functions of a Given Convex Function, Scalar and Vector Optimization in Economic and Financial Problems, Edited by E. Castagnoli and G. Giorgi, Elioprint, Milan, Italy, pp. 135–143, 1995.
Dragominescu, M., andIvan, C.,The Smallest Convex Extension of a Convex Function, Optimization, Vol. 24, pp. 193–206, 1992.
Baiocchi, C., andCapelo, A.,Variational and Quasivariational Inequalities, John Wiley, New York, New York, 1984.
Giannessi, F.,Separation of Sets and Gap Functions for Quasivariational Inequalities, Variational Inequalities and Network Equilibrium Problems, Edited by F. Giannessi and A. Maugeri, Plenum, New York, New York, pp. 101–121, 1995.
Author information
Authors and Affiliations
Additional information
Communicated by F. Giannessi
Rights and permissions
About this article
Cite this article
Pellegrini, L. Coercivity and image of constrained extremum problems. J Optim Theory Appl 89, 175–188 (1996). https://doi.org/10.1007/BF02192647
Issue Date:
DOI: https://doi.org/10.1007/BF02192647