Dualität bei Optimierungsaufgaben in halbgeordneten topologischen Vektorräumen (I): Duality in optimization problems in partially ordered topological vector spaces (I)

W. W. Breckner

doi:10.33993/jnaat11-1

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W. W. Breckner "Babeş Bolyai" University, Cluj-Napoca, Romania

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https://doi.org/10.33993/jnaat11-1

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MR0378809 (51 #14975)
Zbl 0374.90071

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References

Altman, M., Théorème général de séparation des applications. Dualité dans la programmation mathématique. Fonctions duales. C. R. Acad. Sci. Paris Sér. A-B 269 1969 A198-A201, (French) MR0249107.

Altman, M., A general separation theorem for mappings, saddle-points, duality and conjugate functions. Studia Math. 36 (1970), 131-167, MR0306940. DOI: https://doi.org/10.4064/sm-36-2-131-167

Arrow, Kenneth J., Hurwicz, Leonid, Uzawa, Hirofumi, Studies in linear and non-linear programming. With contributions by H. B. Chenery, S. M. Johnson, S. Karlin, T. Marschak, R. M. Solow. Stanford Mathematical Studies in the Social Sciences, vol. II. Stanford University Press, Stanford, Calif. 1958 vii+229 pp., MR0108399.

(In Russian)

Blumenthal, B., (Herausgeber), Mathematische Methoden in der Operationsforschung. Berlin, Verlag Die Wirtschaft, 1970 (in German).

Bod, Péter, On linear optimization with several objective functions. Magyar Tud. Akad. Mat. Kutató Int. Közl. 8 1963 541-556 (1964), (Hungarian) MR0198965.

Breckner, W. W., Probleme duale de optimizare în spaţii vectoriale topologice ordonate. Cluj, Academia R.S.R., Filiala din Cluj, Institutul de calcul, Seminarul de cea mai bună aproximaţie şi programare matematică, 24-21 mai 1969.

Breckner, W. W., Teoreme de caracterizare a soluţiilor anumitor probleme de optimizare. Teză de doctorat. Cluj, Univeristatea "Babeş-Bolyai", 1970 (in Romanian).

Breckner, Wolfgang W., Kolumbán, Iosif, Dualität bei Optimierungsaufgaben in topologischen Vektorräumen. Mathematica (Cluj) 10 (33) 1968, 229-244, (in German) MR0250088.

Breckner, Wolfgang W.; Kolumbán, Iosif, Konvexe Optimierungsaufgaben in topologischen Vektorräumen. Math. Scand. 25 1970 227-247, (in German) MR0270239, https://doi.org/10.7146/math.scand.a-10959 DOI: https://doi.org/10.7146/math.scand.a-10959

Brøndsted, A., Conjugate convex functions in topological vector spaces. Mat.-Fys. Medd. Danske Vid. Selsk. 34 1964 no. 2, 27 pp. (1964), MR0166580.

Chang, Sheldon S. L., General theory of optimal processes. SIAM J. Control 4 1966 46-55, MR0197199, https://doi.org/10.1137/0304005 DOI: https://doi.org/10.1137/0304005

Chattopadhyay, R., Linear programming with vector-valued cost function. Honolulu, University of Hawaii, the Aloha System, technical Report, A 70-3, 1970.

Chattopadhyay, R., Well posed linear programs with vector-valued cost functions. Part. II. Honolulu, University of Hawaii, The Aloha system, Technical Report, A 70-5, 1970.

Chattopadhyay, Well posed linear programs with vector-valued cost functions. Part. II. Honolulu, Univeristy of Hawaii, The Aloha system, Technical Report, A 70-5- 1970.

Collatz, Lothar, Wetterling, Wolfgang, Optimierungsaufgaben. Zweite Auflage. Heidelberger Taschenbücher, Band 15. Springer-Verlag, Berlin-New York, 1971. x+222 pp., (in German) MR0347131. DOI: https://doi.org/10.1007/978-3-642-65286-8

da Cunha, N.O., Polak, E. Constrained minimization under vector-valued criteria in finite dimensional spaces. J. Math. Anal. Appl. 19, 103-124 (1967), Zbl 0154.44801, https://doi.org/10.1016/0022-247x(67)90025-x DOI: https://doi.org/10.1016/0022-247X(67)90025-X

Da Cunha, N.O., Polak, E., Constrained minimization under vector-valued criteria in linear topological spaces. Math. Theory Control, Conf. Univ. South. Calif. 1967, 96-108 (1967), Zbl 0223.49012.

Dieter, Ulrich, Dualität bei konvexen Optimierungs-(Programmierungs-)Aufgaben. Unternehmensforsch. 9, 91-111 (1965), (in German) Zbl 0147.38602, https://doi.org/10.1007/bf01919477 DOI: https://doi.org/10.1007/BF01919477

Dieter, Ulrich, Optimierungsaufgaben in topologischen Vektorräumen. I: Dualitätstheorie. Z. Wahrscheinlichkeitstheor. Verw. Geb. 5, 89-117 (1966), (in German) Zbl 0147.38601, https://doi.org/10.1007/bf00536646 DOI: https://doi.org/10.1007/BF00536646

Dieter, Ulrich, Dual extremal problems in locally convex linear spaces. Proc. Colloq. Convexity, Copenhagen 1965, 52-57 (1967), Zbl 0156.18905.

Dieter, Ulrich, Dual extremal problems in linear spaces with examples and applications in game theory and statistics. Erschienen in: Ghizzetti A. (Editor). Theory an Applications of Montone Operators. Gubbio, Ed. Oerisi, 1969, 1-9.

Elsteri, K. H., Ergebnisse und Probleme der Nichtlinearen Optimierung. Wiss. Z. TH Ilmenau, 15, 3, 37-61, 1969 (German).

Elster, K.-H., Suppe, C., Zur Entwicklung der Dualitätstheorie in der nichtlinearen Optimierung. Wiss. Z. Tech. Hochsch. Ilmenau 15, No.4-5, 77-98 (1969), (in German) Zbl 0197.45805.

Fenchel, W., Convex cones, sets and functions. Logistic Project Report. Princeton: Department of Mathematics, Princeton University. (Multilith.) 152 p. (1953), Zbl 0053.12203.

Geoffrion, A.M., Proper efficiency and the theory of vector maximization. J. Math. Anal. Appl. 22, 618-630 (1968), Zbl 0181.22806, https://doi.org/10.1016/0022-247x(68)90201-1 DOI: https://doi.org/10.1016/0022-247X(68)90201-1

Ghika, A., Opera matematică, Bucureşti, Editura Academiei R.S.R., 1968 (in Romanian).

Golstein, E.G., (in Russian)

Gould, F.J., Nonlinear duality theorems. Chicago, Unviersity of Chicago, Center for Math. Studies in business and Economics, Report 6817, April 1968.

Ioffe, A.D., (in Russian)

Karlin, S., Mathematical methjods and theory in games, programming and economics. I. London-Paris, Pergamon press, 1959.

Klinger, A., Vector-valued performance criteria. IEEE Trans. Automat. Control. 9, 117-118, 1964, https://doi.org/10.1109/tac.1964.1105632 DOI: https://doi.org/10.1109/TAC.1964.1105632

Klinger, A., Improper solutions of the vector maximum problem. Operations Res., 15, 570-572, 1967, https://doi.org/10.1287/opre.15.3.570 DOI: https://doi.org/10.1287/opre.15.3.570

Kolumbán, I., Principiul dualităţii la o clasă de probleme de optimizare. Teză de doctorat Cluj, Universitatea "Babeş-Bolyai", 1968 (in Romanian).

Kolumban, I., Dualität bei Optimierungsaufgaben. Proc. Conf. construct. Theory Functions (Approximation Theory) 1969, 261-265 (1972), (in German) Zbl 0261.90054.

Köthe, G., Topologische lineare Räume, I.2. Auflage. Berlin - Heidelbergh - New York, Springer - Verlag, 1966 (in German) DOI: https://doi.org/10.1007/978-3-662-24912-3

Krabs, Werner, Lineare Optimierung in halbgeordneten Vektorräumen. Numer. Math. 11, 220-231 (1968), (in German) Zbl 0262.90034, https://doi.org/10.1007/bf02161844 DOI: https://doi.org/10.1007/BF02161844

Krabs, W., Zur Dualitätstheorie bei linearen Optimierungsproblemen in halbgeordneten Vektorräumen. Math. Z. 121, 320-328 (1971), (in German) Zbl 0213.45101, https://doi.org/10.1007/bf01109978 DOI: https://doi.org/10.1007/BF01109978

Kuhn, H.W., Tucker, A.W., Nonlinear programming. Proc. Berkeley Sympos. math. Statist. Probability, California July 31 - August 12, 1950, 481-492 (1951), Zbl 0044.05903.

Leonte, A., Le problème de la programmation concave dans les espaces Hilbert ordonnés. An. Univ. Bucureşti, Ser. Şti. Natur., Mat.-Mec. 17, No.2, 147-149 (1968), (in Romanian) Zbl 0211.22401.

Moreau, J. J., Fonctionnelles convexes. Collège de France, Séminaire sur les équations aux dérivées partielles, 1967 (French).

Peressini, A.L., Ordered topological vector spaces. New York-Evanston-London: Harper and Row Publishers 1967. X, 228 p. (1967), Zbl 0169.14801.

Philip, J., Algorithms for the vector maximization problem. Math. Programming, 2, 207-229, 1972, https://doi.org/10.1007/bf01584543 DOI: https://doi.org/10.1007/BF01584543

Rockafellar, R.T., Extension of Fenchel's duality theorem for convex functions. Duke Math. J. 33, 81-89 (1966), Zbl 0138.09301, https://doi.org/10.1215/s0012-7094-66-03312-6 DOI: https://doi.org/10.1215/S0012-7094-66-03312-6

Rockafellar, R.T., Duality and stability in extremum problems involving convex functions. Pac. J. Math. 21, 167-187 (1967), Zbl 0154.44902, https://doi.org/10.2140/pjm.1967.21.167 DOI: https://doi.org/10.2140/pjm.1967.21.167

Rockafellar, R. T., Convex analysis, Princenton, Princeton Unviersity Press, 1970. DOI: https://doi.org/10.1515/9781400873173

Roy, B., Problems and methods with multiple objective functions. Math. Program. 1, 239-266 (1971), Zbl 0254.90061, https://doi.org/10.1007/bf01584088 DOI: https://doi.org/10.1007/BF01584088

Rubinstein - (in Russian)

Rudeanu, S., Programmation bivalente à plusieures fonctions économiques. Rev. Franç. Inform. Rech. Opér. 3, No.V-2, 13-30 (1969), (French) Zbl 0205.22001, https://doi.org/10.1051/ro/196903v200131 DOI: https://doi.org/10.1051/ro/196903V200131

Stoer, Josef, Witzgall, Christoph, Convexity and optimization in finite dimensions. Berlin-Heidelberg-New York: Springer-Verlag. IX, 293 p. (1970), Zbl 0203.52203. DOI: https://doi.org/10.1007/978-3-642-46216-0

(in Russian)

Vogel, W., Duale Optimierungsaufgaben und Sattelpunktsätze. Unternehmensforsch. 13, 1-28 (1969), (in German) Zbl 0169.22003, https://doi.org/10.1007/bf01919547 DOI: https://doi.org/10.1007/BF01919547

Weiss, E. A., Konjugierte Funktionen. Arch. der Masth. 20, 538-545, 1969, (in German) https://doi.org/10.1007/bf01899461 DOI: https://doi.org/10.1007/BF01899461

Yamasaki, M., Duality theorems in mathematical programmings and their applications. J. Sci. Hiroshima Univ., Ser. A-I 32, 331-356 (1968), Zbl 0179.24502, https://doi.org/10.32917/hmj/1206138657 DOI: https://doi.org/10.32917/hmj/1206138657

Yamasaki, M., Some generalizations of duality theorems in mathematical programming problems. Math. J. Okayama Univ. 14, 69-81 (1969), Zbl 0205.21703.