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Mathematical programming problems involving continuum of inequality constraints. (English) Zbl 0487.49019
MSC:
49M37 Numerical methods based on nonlinear programming
90C55 Methods of successive quadratic programming type
49K35 Optimality conditions for minimax problems
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
90C25 Convex programming
90C30 Nonlinear programming
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References:
[1] V. G. Boltyanskii: Optimal Control of Discrete Systems. (in Russian). Nauka, Moscow 1973.
[2] K. R. Gehner: Necessary and sufficient conditions for the Fritz John problem with linear equality constraints. SIAM J. Control 72 (1974), 1, 140-149. · Zbl 0253.49019
[3] J. Doležal: On mathematical programming problems with infinitely many inequality constraints. Internat. J. Systems Sci.
[4] W. E. Schmitendorf: A simple derivation of necessary conditions for static minmax problems. J. Math. Ana!. Appl. 70 (1979), 2, 486-489. · Zbl 0435.49029
[5] J. Doležal: On necessary conditions for static minmax problems with constraints. J. Math. Anal. Appl. 55 (1982), 2.
[6] M. D. Canon C. D. Cullum E. Polak: Theory of Optimal Control and Mathematical Programming. McGraw-Hill, New York 1970. · Zbl 0264.49001
[7] V. G. Boltyanskii: The method of tents in the theory of extremal problems. (in Russian). Uspekhi Matematicheskikh Nauk XXX (1975), 3,3 - 55. · Zbl 0318.49017
[8] B. M. Kwak E. J. Huag, Jr.: Optimum design in presence of parametric uncertainty. J. Optim. Theory Appl. 19 (1976), 4, 527-546. · Zbl 0309.49005
[9] V. G. Boltyanskii I. S. Čebotaru: Necessary conditions in a minmax problem. (in Russian). Doklady Akademii Nauk SSSR 213 (1973), 2, 257-260.
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