Theorem of Motzkin's alternative for nonhomogeneous complex linear equations and inequalities
Abstract
Not available.Downloads
References
Abrams, Robert A.; Ben-Israel, Adi Nonlinear programming in complex space: necessary conditions. SIAM J. Control 9 (1971), pp. 606-620, MR0378816, https://doi.org/10.1137/0309043
Ben-Israel, Adi Linear equations and inequalities on finite dimensional, real or complex, vector spaces: A unified theory. J. Math. Anal. Appl. 27 1969, pp. 367-389, MR0242865, https://doi.org/10.1016/0022-247x(69)90054-7
Ben-Israel, A. Erratum: "Theorems of the alternative for complex linear inequalities". Israel J. Math. 7 1969 292a, MR0260426, https://doi.org/10.1007/bf02771659
Abrams, Robert A.; Ben-Israel, Adi On the key theorems of Tucker and Levinson for complex linear inequalities. J. Math. Anal. Appl. 29 1970, pp. 640-646, MR0252419, https://doi.org/10.1016/0022-247x(70)90072-7
Craven, B. D.; Mond, B. A Fritz John theorem in complex space. Bull. Austral. Math. Soc. 8 (1973), pp. 215-220, MR0319020, https://doi.org/10.1017/s0004972700042465
Craven, B. D.; Mond, B. Real and complex Fritz John theorems. J. Math. Anal. Appl. 44 (1973), pp. 773-778, MR0359774, https://doi.org/10.1016/0022-247x(73)90016-4
Craven, B. D.; Mond, B. On duality in complex linear programming. Collection of articles dedicated to the memory of Hanna Neumann, II. J. Austral. Math. Soc. 16 (1973), pp. 172-175, MR0337309, https://doi.org/10.1017/s144678870001418x
Dragomirescu, M. şi Maliţa, M., Programare neliniară, Ed. ştiinţifică, Bucureşti, 1972.
Duca, Dorel I. On vectorial programming problem in complex space. Studia Univ. Babeş-Bolyai Math. 24 (1979), no. 1, pp. 51-56, MR0574563.
Duca, Dorel I. Necessary optimality criteria in nonlinear programming in complex space with differentiability. Anal. Numér. Théor. Approx. 9 (1980), no. 2, pp. 163-179 (1981), MR0651772.
Duca, D.I., Mathematical programming in complex space, Doctoral thesis, Unviersity of Cluj-Napoca, Cluj-Napoca, 1981.
Duca, Dorel I. Efficiency criteria in vectorial programming in complex space without convexity. Cahiers Centre Études Rech. Opér. 26 (1984), no. 3-4, pp. 217-226, MR0778105.
Duca, Dorel I. On the Farkas type theorem for complex linear equations and inequalities. Itinerant Seminar on Functional Equations, Approximation and Convexity (Cluj-Napoca, 1987), pp. 143-148, Preprint, 87-6, Univ. "Babeş-Bolyai", Cluj-Napoca, 1987, MR0993526.
Duca, Dorel I. On theorems of the alternative for nonhomogeneous complex linear equations and inequalities. Seminar on Optimization Theory, 29-40, Preprint, 87-8, Univ. "Babeş-Bolyai", Cluj-Napoca, 1987, MR0977089.
Farkas, J., Über die Theorie der einfachen Ungleichungen, J. Reine Angew. Math., 124 (1902), pp. 1-24.
Gordan, P.; Ueber die Auflösung linearer Gleichungen mit reellen Coefficienten. (German) Math. Ann. 6 (1873), no. 1, pp. 23-28, MR1509805, https://doi.org/10.1007/bf01442864
Gulati, T. R. A Fritz John type sufficient optimality theorem in complex space. Bull. Austral. Math. Soc. 11 (1974), pp. 219-224, MR0368778, https://doi.org/10.1017/s0004972700043811
Kaul, R. N. On linear inequalities in complex space. Amer. Math. Monthly 77 1970, pp. 956-960, MR0268209.
Levinson, Norman Linear programming in complex space. J. Math. Anal. Appl. 14 1966, pp. 44-62, MR0225569, https://doi.org/10.1016/0022-247x(66)90061-8
Mangasarian, Olvi L. Nonlinear programming. McGraw-Hill Book Co., New York-London-Sydney 1969 xiii+220 pp., MR0252038.
Mond, Bertram An extension of the transposition theorems of Farkas and Eisenberg. J. Math. Anal. Appl. 32 1970, pp. 559-566, MR0269315, https://doi.org/10.1016/0022-247x(70)90277-5
Mond, Bertram; Hanson, Morgan A. A complex transposition theorem with applications to complex programming. Linear Algebra and Appl. 2 1969, pp. 49-56, MR0243818, https://doi.org/10.1016/0024-3795(69)90006-8
Mond, Bertram; Hanson, Morgan A. Some generalizations and applications of a complex transposition theorem. Linear Algebra and Appl. 2 1969, pp. 401-411, MR0253740, https://doi.org/10.1016/0024-3795(69)90013-5
Motzkin, T.S., Beiträge zur Theorie der linearen Ungleichiben, Inaugural Dissertation, Basel 1933; Jerusalem, Azriel, 1936 (English translation: U.S. Air Force-Proiect Rand, Report T-22, 1952).
Stancu-Minasian, I.M. and Duca, D.I., Multiple objective linear fractional optimization in complex space (to appear).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
