Constrained extremum problems with infinite-dimensional image: Selection and necessary conditions. (English) Zbl 1126.49005
Summary: This paper deals with image space analysis for constrained extremum problems having an infinite-dimensional image. It is shown that the introduction of selection for point-to-set maps and of quasi multipliers allows one to establish optimality conditions for problems where the classical approach fails.
MSC:
| 49J40 | Variational inequalities |
| 90C46 | Optimality conditions and duality in mathematical programming |
| 49M37 | Numerical methods based on nonlinear programming |
References:
| [1] | Giannessi, F.: Theorems of the alternative for multifunctions with applications to optimization: general results. J. Optim. Theory Appl. 55(2), 233–256 (1987) · Zbl 0622.90084 · doi:10.1007/BF00939083 |
| [2] | Giannessi, F.: Constrained Optimization and Image Space Analysis, vol. 1: Separation of Sets and Optimality Conditions. Springer, New York (2005) · Zbl 1082.49001 |
| [3] | Giannessi, F., Mastroeni, G., Uderzo, A.: A multifunction approach to extremum problems having infinite dimensional image: necessary conditions for unilateral constraints. Cybern. Syst. Anal. 3, 39–51 (2003) · Zbl 1176.90650 |
| [4] | Pars, L.A.: An Introduction to the Calculus of Variations. Heinemann, London (1962) · Zbl 0108.10303 |
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