×

Refinements of necessary optimality conditions in nondifferentiable programming. I. (English) Zbl 0389.90088


MSC:

90C30 Nonlinear programming
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] E. J. Beltrami, A constructive proof of the Kuhn-Tucker multiplier rule,J. Math. Anal. Appl., 26, 297-306 (1969). · Zbl 0232.90051
[2] E. J. Beltrami, An algorithmic approach to nonlinear analysis and optimization, Academic Press, New York and London, 1970. · Zbl 0207.17202
[3] C. Berge, Espaces topologiques, fonctions multivoques, Dunod, Paris, 1966. · Zbl 0164.52902
[4] F. H. Clarke, Generalized gradients and applications,Transactions of the American Math. Society, 205, 247-262 (1975). · Zbl 0307.26012
[5] F. H. Clarke, A new approach to Lagrange multipliers,Math. of Operations Res., 2, 165-174 (1976). · Zbl 0404.90100
[6] F. H. Clarke, On the inverse function theorem,Pacific J. Math., 64, 97-102 (1976). · Zbl 0331.26013
[7] F. H. Clarke, Inequality constraints in the calculus of variations,Can. J. Math., 29, 3, 528-540 (1977). · Zbl 0346.49014
[8] G. B. Dantzig, J. Folkman and N. Shapiro, On the continuity of the minimum set of a continuous function,J. Math. Anal. Appl., 17, 519-548 (1967). · Zbl 0153.49201
[9] M. R. Hestenes, Optimization Theory: the finite dimensional case, J. Wiley and Sons, 1975. · Zbl 0327.90015
[10] J-B. Hiriart-Urruty, Conditions nécessaires d’optimalité en programmation non différentiable, Note auxComptes Rendus Acad. Sc. Paris t. 283, Serie A, 843-845 (1976).
[11] J-B. Hiriart-Urruty, On necessary optimality conditions in nondifferentiable programming,Math. Programming, 14, 1 73-86 (1978). · Zbl 0373.90071
[12] J-B. Hiriart-Urruty, Tangent cones, generalized gradients and mathematical programming in Banach spaces,Math. of Operations Res., to be published (1978).
[13] J-B. Hiriart-Urruty, Gradients généralisés de fonctions composées, Applications. Note auxComptes Rendus Acad. Sc. Paris t. 285, Serie A, 781-784 (1977).
[14] J-B. Hiriart-Urruty, New concepts in nondifferentiable programming,Journées d’Analyse Non Convexe (Mai 1977), Université de Pau (France); to be published (1978).
[15] O. L. Mangasarian and S. Fromovitz, The Fritz John necessary optimality conditions in the presence of equality and inequality constraints,J. Math. Anal. Appl., 17, 37-47 (1967). · Zbl 0149.16701
[16] J-M. Ortega and W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Acad. Press, New York and London, 1970. · Zbl 0241.65046
[17] B. Pourciau, Analysis and optimization of Lipschitz continuous mappings,J. of Optim. Theory and Applications, 22, 311-351 (1977). · Zbl 0336.26008
[18] R. T. Rockafellar, Convex analysis, Princeton University Press, 1970. · Zbl 0193.18401
[19] E. J. McShane, The Lagrange multiplier rule,American Mathematical Monthly, 80, 922-925 (1973). · Zbl 0294.26016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.