Tangent sets of order one and two to the positive cones of some functional spaces

Applied Mathematics and Optimization

Volumn 36, Issue 3, 1997, Pages 291-312

  Cominetti, R ^a   Penot, J P ^b  

^a UNIVERSITY OF CHILE   (Chile)

^b CNRS   (France)

Author keywords

Epiconvergence; Optimality conditions; Positive cone; Tangent sets

Indexed keywords

DIFFERENTIATION (CALCULUS); OPTIMIZATION; SET THEORY;

OPTIMALITY CONDITIONS; TANGENT SETS;

FUNCTIONS;

EID: 0031281748     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002459900064     Document Type: Article

References (20)

1. Aubin J-P, Frankowska H (1990), Set-Valued Analysis, Birkhäuser, Boston.
2. Attouch H (1984), Variational Convergences for Functions and Operators, Pitman Advanced Publishing Program, London.
3. Ben-Tal A, Zowe J (1982), A unified theory of first- and second-order conditions for extremum problems in topological vector spaces, Mathematical Programming Studies 19:39-76.
4. Ben-Tal A, Zowe J (1982), Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems, Mathematical Programming 24(1):70-91.
5. 1-minimization problem, Applied Mathematics and Optimization 13(1):45-58.
6. Cioranescu D, Murat F (1982), Un terme étrange venu d'ailleurs I, II, in Nonlinear Partial Differential Equations and Their Applications, Collège de France Seminar, vol II, Pitman, London, pp 98-138.
7. Cominetti R (1990), Metric regularity, tangent sets, and second-order optimality conditions, Applied Mathematics and Optimization 21:265-287.
8. Dunford N, Schwartz J-T (1988), Linear Operators. Part I: General Theory, Classics Library Edition, Wiley, New York.
9. Giner E (1985), Etude des fonctionnelles intégrales, Thesis, Université de Pau.
10. Ioffe A (1991), Variational analysis of a composite function: a formula for the lower second-order epi-derivative, Journal of Mathematical Analysis and Applications 160(2):379-405.
11. Ioffe A (1993), Variational analysis of a composite function: perturbations, value function, and sensitivity, Preprint, Haifa MT 880.
12. Kawasaki H (1988), An envelope-like effect of infinitely many inequality constraints on second-order necessary conditions for minimization problems, Mathematical Programming 41:73-96.
13. Kawasaki H (1988), The upper and lower second-order directional derivative of a sup-type function, Mathematical Programming 41:327-339.
14. Kawasaki H (1991), Second-order necessary optimality conditions for minimizing a sup-type function, Mathematical Programming 49:213-229.
15. Murat F (1978), H-convergence, rapport du Séminaire d'Analyse Fonctionnelle et Numérique de l'Université d'Alger.
16. Penot J-P (1984), Generalized higher-order derivatives and higher-order optimality conditions, Manuscript.
17. Penot J-P (1990), Optimality conditions in mathematical programming, Preprint, Université de Pau, Optimisation 90/30.
18. Penot J-P (1990), Optimality conditions for composite functions, Preprint, Université de Pau, Optimisation 90/25.
19. Rao M, Sokolowski J (1991), Differential stability of solutions to parametric optimization problems, Mathematical Methods in the Applied Sciences 14:281-294.
20. Rockafellar R-T (1976), Integral functionals, normal integrands, and measurable selections, in Nonlinear Operators and the Calculus of Variations, L Walbroeck, ed, Lecture Notes in Mathematics, vol. 543, Springer-Verlag, Berlin, pp 157-207.