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A strengthened test for optimality. (English) Zbl 0473.90066

MSC:
90C25 Convex programming
49M29 Numerical methods involving duality
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[1] Abrams, R. A., andKerzner, L.,A Simplified Test for Optimality, Journal of Optimization Theory and Applications, Vol. 25, pp. 161-170, 1978. · Zbl 0352.90047
[2] Ben-israel, A., Ben Tal, A., andZlobec, S.,Optimality Conditions in Convex Programming, IX International Symposium on Mathematical Programming, Budapest, Hungary, 1976. · Zbl 0352.90048
[3] Rockafellar, R. T.,Some Convex Programs Whose Duals Are Linearly Constrained, Nonlinear Programming, Edited by J. B. Rosen, O. L. Mangasarian, and K. Ritter, Academic Press, New York, New York, pp. 293-322, 1970. · Zbl 0252.90046
[4] Gould, F. J., andTolle, J. W.,Geometry of Optimality Conditions and Constraint Qualifications, Mathematical Programming, Vol. 2, pp. 1-18, 1972. · Zbl 0288.90068
[5] Geoffrion, A. M.,Duality in Nonlinear Programming: A Simplified Application-Oriented Development, SIAM Review, Vol. 13, pp. 1-37, 1971. · Zbl 0232.90049
[6] Wolkowicz, H. Shadow Prices for an Unstable Convex Program, Utilitas Mathematica (to appear). · Zbl 0458.90053
[7] Wolkowicz, H.,Geometry of Optimality Conditions and Constraint Qualifications: The Convex Case, Mathematical Programming, Vol. 19, pp. 32-60, 1980. · Zbl 0436.90082
[8] Holmes, R. B.,Geometric Functional Analysis and Its Applications, Springer-Verlag, Berlin, Germany, 1975. · Zbl 0336.46001
[9] Borwein, J., andWolkowicz, H.,Characterizations of Optimality without Constraint Qualification for the Abstract Convex Program, Dalhousie University, Halifax, Canada, Research Report No. 14, 1979.
[10] Borwein, J., andWolkowicz, H.,Characterizations of Optimality for the Abstract Convex Program with Finite-Dimensional Range, Journal of the Australian Mathematical Society (to appear). · Zbl 0469.90088
[11] Borwein, J., andWolkowicz, H.,Regularizing the Abstract Convex Program, Journal of Mathematical Analysis and Applications (to appear). · Zbl 0467.90076
[12] Dubovitskii, A. Ja., andMilyutin, A. A.,Extremum Problems in the Presence of Restrictions, Vol. 5, pp. 1-80, 1965. · Zbl 0158.33504
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