An Approach to Optimality Conditions in Vector and Scalar Optimization
The implication of concavity in economics have suggested in the scalar case several kinds of generalization starting from the pioneering work of Arrow-Enthoven (1961).
The aim of this paper is to point out the role played by generalized concavity and by the tangent cone to the feasible region at a point, in stating several necessary and/or sufficient optimality conditions for a vector and scalar optimization problem.
Furthermore, in deriving F.John optimality conditions, the role of separations theorems is analyzed in order to suggest suitable formulations of Kuhn-Tucker conditions and a way for studying regularity conditions.
Unable to display preview. Download preview PDF.
- Arrow, K.J and Enthoven, A.C (1961) “Quasi concave Programming” Econometrica 29, 779–800Google Scholar
- Cambini A., Martein, L. (1991): “Optimality conditions in vector and scalar optimization”, report 50, Dept of Statistics and Applied Mathematics, University of Pisa, 1991.Google Scholar
- Cambini, R. (1992): “Alcune condizioni di ottimalitk relative ad un insieme stellato”, report 54, Dept. of Statistics and Applied Mathematics, University of Pisa, 1992.Google Scholar
- Mangasarian, O. L. (1969): Nonlinear Programming, McGraw-Hill, New York.Google Scholar
- Rockafellar, R. T. (1970): Convex Analysis, Princeton, New Jersey.Google Scholar