×

Polyextremal principles and separably-infinite programs. (English) Zbl 0451.90082


MSC:

90C05 Linear programming
91A05 2-person games
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bracken, J., J. Falk, andJ. T. McGill: Equivalence of Two Mathematical Programs with Optimization Problems in the Constraints. Institute for Defense Analysis Paper 969, Log HQ73-15312, Program Analysis Division, 1973.
[2] Bracken, J., andJ. T. McGill: Mathematical Programs with Optimization Problems in the Constraints. Operations Research21, 1973, 37–44. · Zbl 0263.90029 · doi:10.1287/opre.21.1.37
[3] Charnes, A.: Constrained Games and Linear Programming. Proc. Nat. Acad. Sci., USA38, 1953, 639–641. · Zbl 0050.14101 · doi:10.1073/pnas.39.7.639
[4] Charnes, A., andW. W. Cooper: An Extremal Principle for Accounting Balance of a Resource Value-Transfer Economy: Existence, Uniqueness, and Computation. Accademia Nazionale Dei Lincei, Serie VIII,LVI, 1974, 556–561. · Zbl 0322.90014
[5] Charnes, A..W.W. Cooper, andK.O. Kortanek: Duality, Haar Programs, and Finite Sequence Spaces. Proc. Nat. Acad. Sci., USA68, 1962, 605–608. · Zbl 0131.36502
[6] Charnes, A., P.R. Gribik, andK.O. Kortanek: Separably-Infinite Programs. Zeitschrift für Operations Research24, 1980, 33–45. · Zbl 0426.90055 · doi:10.1007/BF01920270
[7] Danskin, J.M.: The Theory of Max-Min. New York 1967. · Zbl 0154.20009
[8] Debreu, G.: Theory of Value, An Axiomatic Analysis of Economic Equilibrium. New York 1959. · Zbl 0193.20205
[9] Fahlander, K.: Computer Programs for Semi-infinite Optimization. Swedish Institute for Applied Mathematics, Stockholm TRITA-NA-7312, 1973.
[10] Fan, K.: Asymptotic Cones and Duality of Linear Relations. J. Approximation Theory2, 1969, 152–159. · Zbl 0174.17801 · doi:10.1016/0021-9045(69)90038-0
[11] Glashoff, K.: Duality Theory of Semi-infinite Programming. Semi-Infinite Programming. Ed. by R. Hettrich. Lecture Notes in Control and Information Sciences, ed. by A.V. Balakrishnan and M. Thomas, Berlin-Heidelberg-New York 1979. · Zbl 0417.90073
[12] Glashoff, K., andS.-Å. Gustafson: Einführung in die Lineare Optimierung, Darmstadt 1978. · Zbl 0393.90054
[13] Gol’stein, E.G.: Theory of Convex Programming. Translations of Mathematical Monographs, American Mathematical Society. Vo. 36, 1972, Providence, Rhode Island.
[14] Gustafson, S.-Å., andK.O. Kortanek: Numerical Solution of a Class of Semi-infinite Programming Problems. Naval Research Logistics Quarterly20, 1973, 477–504. · Zbl 0272.90073 · doi:10.1002/nav.3800200310
[15] Krabs, W.: Optimierung und Approximation. Stuttgart 1975. · Zbl 0321.41017
[16] Rockafellar, R.T.: Convex Analysis. Princeton, New Jersey 1970. · Zbl 0193.18401
[17] Stoer, J., andC. Witzgall: Convexity and Optimization in Finite Dimensions I. New York 1970. · Zbl 0203.52203
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.