Mathematical programming in complex space: a comprehensive bibliography

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  • Dorel I. Duca "Babeş-Bolyai" University, Cluj-Napoca, Romania
  • I. M. Stancu-Minasian Academyc of Economic Studies, Bucharest, Romania
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References

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Abrams, R. S., Mathematical programming in complex variables: applications to electrical engineering, Mem.Conf. Int. IEEE Sist., Redes y Comp., Oaxtepec, Mor. (Mex), 1971, Vol. 2, S1, 787-792.

Abrams, Robert A., Nonlinear programming in complex space: Sufficient conditions and duality. (English) J. Math. Anal. Appl. 38, 619-632 (1972)., Zbl 0265.90050, https://doi.org/10.1016/0022-247x(72)90073-x

Abrams, R.A., Ben-Israel, Adi., A duality theorem for complex quadratic programming. (English) J. Optimization Theory Appl. 4, 244-252 (1969), Zbl 0172.43703, https://doi.org/10.1007/bf00927948

Abrams, R. A., Ben-Israel, Adi, Complex mathematical programming, Report No. 69-11, Northwestern Univ. Evanston, Illinois, November, 1969.

Abrams, R. A., Ben-Israel, Adi, Nonlinear programming in complex space: necessary conditions, Report No. 70-73, Series in applied Mathematics, NorthwesternUniv., Evanston, Illinois, 1970.

Abrams, R. A. and Ben-Israel, Adi, Nonlinear programming in complex space: necessary conditions, SIAM J. Control. 0, 1071, no. 4, 606-620.

Abrams, R. A. and Ben-Israel, Adi, Complex mathematical programming, in: Developments in operations research, B. Avi-Itzhak (ed) 3-20, Gordon and Breach, New York, 1971.

Alders, D. C., Sposito, V. A., A note on "Real and complex Fritz John theorems". (English) J. Math. Anal. Appl. 67, 92-93 (1979), Zbl 0396.49010, https://doi.org/10.1016/0022-247x(79)90008-8

Bector, G. R. and Bhatia, S. K., Generalized duality for nonlinear programming in complex space, Econom. comput. Econom. Cybernet. Stud. Res., 20, 1985, no. 2, 75-80.

Bector, C. R., Bhatt, S.K., Nonlinear programming in complex space: Necessary and sufficient conditions. (English) Rev. Roum. Math. Pures Appl. 30, 497-503 (1985), Zbl 0584.90081.

Bector, C. R., Chandra, Suresh; Gulati, T.R., Duality for complex nonlinear fractional programming over cones. (English) Proc. 3rd Manitoba Conf. numer. Math., Winnipeg 1973, 87-103 (1974),Zbl 0323.90052.

Bector, C. R., Chandra, Suresh, and Gulati, T. R., Complex nonlinear programming with equality constraints, Proceedings of the Foruth Manitoba Conference on Numerical Mathematics held in Winnipeg (Manitoba, October 2-5, 1974), pp. 205-216, Congressus Numeratium, No. XII, Utilitas Math, Publishing Inc., Winnipeg, Man., 1975.

Bector, C. R., Chandra, Suresh and gulati, T R., A lagrangian approach to duality for complex fractional programming over cones, Math. Operationsforsch. Statist., Ser. Optimizaiton, 8, 1977, no.1, 17-25, https://doi.org/10.1080/02331937708842402

Ben-Israel, Adi, Linear equations inequalities on finite dimensional, real of complex, vector spaces: a unified theory, J. Math. Anal. Appl., 27, 1969, no. 2, 367-389, https://doi.org/10.1016/0022-247x(69)90054-7

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Ben-Israel, Adi, On cone-monotonicity of complex matrices, SIAM Rev., 12, 1970,, no.1, 120-123, https://doi.org/10.1137/1012009

Ben-Israel, Adi, Linear inequalities and mathematical programming in finite dimensional complex space: theory and applications, Séminaire sur la convexité et ses applications (Quebec, Canada, March 23-25, 1970), p. 1-63, Université de Montreal.

Abrams, R.A., Ben-Israel, A., On the key theorem of Tucker and Levison for complex linear inequalities. (English) J. Math. Anal. Appl. 29, 640-646 (1970), Zbl 0186.33502, https://doi.org/10.1016/0022-247x(70)90072-7

Berman, A., LKinear inequalities over complex cones, Canad. Math. Bull., 16, 1973, no.1, 19-21, https://doi.org/10.4153/cmb-1973-005-x

Berman, A., Genralized interval programming, Bull. Calcutta Math. Soc., 71, 1979, no. 3, 169-176.

Bhatia, D., symmetric dual non-linear programs in complex space, Annual Number, Calcutta Branch of Operational Research Society of India Bulletin, 1, 1968-1968, 131-137.

Bhatia, Davinder, Kaul, R.N., Nonlinear programming in complex space. (English) J. Math. Anal. Appl. 28, 144-152 (1969), Zbl 0222.90040, https://doi.org/10.1016/0022-247x(69)90117-6

Borwein, J.M., A note on Fritz John sufficiency. (English) Bull. Aust. Math. Soc. 15, 293-296 (1976), Zbl 0351.90059.

Craven, B.D., Mond, B., Converse and symmetric duality in complex nonlinear programming. (English) J. Math. Anal. Appl. 37, 617-626 (1972), Zbl 0298.90057.

Craven, B. D., and Mond, B., A Fritz John theorem in complex space, Bull. Austral. Math. Soc., 8, 1973, no. 2, 215-229, https://doi.org/10.1017/s0004972700042465

Craven, B.D., Mond, B., Real and complex Fritz John theorems. (English)J. Math. Anal. Appl. 44, 773-778 (1973), Zbl 0268.49016, https://doi.org/10.1016/0022-247x(73)90016-4

Craven, B.D., Mond, B., On duality in complex linear programming. (English) J. Aust. Math. Soc. 16, 172-175 (1973), Zbl 0283.90031, https://doi.org/10.1017/s144678870001418x

Craven, B.D., Mond, B., Complementarity for arbitrary cones. (English)Z. Oper. Res., Ser. A 21, 143-150 (1977), Zbl 0362.90098, https://doi.org/10.1007/bf01919770

Das, C., Some aspects of quadratic programming in complex space. (English) Z. angew. Math. Mech. 55, 583-587 (1975), Zbl 0324.90059, https://doi.org/10.1002/zamm.19750551005

Das, C., On symmetric duality in complex nonlinear programming. (English) Pure Appl. Math. Sci. 4, 183-189 (1976), Zbl 0351.90060.

Das, C., A duality theory for non-linear non-differentiable complex programming. (English) Acta Cienc. Indica 3, 83-88 (1977), Zbl 0379.90095.

Das, C., A general class of nonlinear complex programming: Necessary and sufficient conditions. (English) Z. Angew. Math. Mech. 59, 393-395 (1979), Zbl 0411.90060, https://doi.org/10.1002/zamm.19790590812

Das, C., A duality theory of a general class of nonlinear complex programming. (English) Z. Angew. Math. Mech. 59, 484-485 (1979), Zbl 0443.90077, https://doi.org/10.1002/zamm.19790590917

Das, C., Parida, J., A duality theorem for complex nonlinear programming. (English) Mat. Vesn., N. Ser. 14(29), 327-332 (1977), Zbl 0369.90105.

Das, C., Swarup, Kanti, Complex fractional functions programming with nonlinear constraints. (English) Z. angew. Math. Mech. 55, 441-442 (1975), Zbl 0317.90052, https://doi.org/10.1002/zamm.19750550715

Das, C., Swarup, K., Nonlinear complex programming with nonlinear constraints. (English) Z. angew. Math. Mech. 57, 333-338 (1977), Zbl 0362.90081, https://doi.org/10.1002/zamm.19770570610

Das, C., Swarup, K., A class of nonlinear nondifferentiable complex programming. (English) Z. angew. Math. Mech. 57, 481-484 (1977), Zbl 0375.90065, https://doi.org/10.1002/zamm.19770570809

Datta, Neelam, A subgradient duality theorem in complex space. (English) Opsearch 21, 16-22 (1984), Zbl 0563.90087.

Datta, Neelam, Non-differentiable mathematical programming in complex space. (English) Opsearch 22, 42-48 (1985), Zbl 0559.90083.

Datta, Neelam, Bhatia, Davinder, A note on minimax (maximin) problems in complex space. (English) Opsearch 17, 110-117 (1980), Zbl 0472.90084.

Datta, Neelam, Bhatia, Davinder, Duality for a class of nondifferentiable mathematical programming problems in complex space. (English) J. Math. Anal. Appl. 101, 1-11 (1984), Zbl 0597.90073.

Datta, Neelam, Bhatia, Davinder, A note on duality theory for concave convex fractional programming problem in complex space. (English) Indian J. Pure Appl. Math. 15, 1289-1295 (1984), Zbl 0573.90091.

Duca, Dorel, Constraint qualifications in nonlinear programming in complex space. (English) Studia Univ. Babes-Bolyai, Math. 23, No.1, 61-65 (1978), Zbl 0381.90089.

Duca, Dorel I., The vectorial programming problem in complex space. (English) Operations research, Proc. 3rd Colloq., Cluj-Napoca/Rom. 1978, 82-89 (1979), Zbl 0491.90086.

Duca, Dorel I., On vectorial programming problem in complex space. (English) Stud. Univ. Babes-Bolyai, Math. 24, No.1, 51-56 (1979), Zbl 0422.90076.

Duca, Dorel I., Proper efficiency in the complex vectorial programming. (English)Stud. Univ. Babes-Bolyai, Math. 25, No.1, 73-80 (1980), Zbl 0446.90082.

Duca, Dorel, I., O teoremă de punct-şa în programarea matematică în domeniul complex, Lucrările seminarului itinerant de ecuaţii funcţionale, aproximare şi convexitate, Cluj-Napoca, mai 1980, 35-39, Univ. Babeş-Bolyai, Cluj-Napoca, 1980.

Duca, Dorel I., Necessary optimality criteria in nonlinear programming in complex space with differentiability. (English)Math., Rev. Anal. Numér. Théor. Approximation, Anal. Numér. Théor. Approximation 9, 163-179 (1980), Zbl 0466.90074.

Duca, Dorel I., Saddlepoint optimality criteria of nonlinear programming in complex space without differentiability. (English) Stud. Univ. Babes-Bolyai, Math. 25, No.4, 39-46 (1980), Zbl 0457.90063.

Duca, Dorel I., On sufficient optimality conditions in nonlinear programming in complex space. (English) Math., Rev. Anal. Numér. Théor. Approximation, Math. 22(45), 263-267 (1980), Zbl 0478.90064.

Duca, Dorel I., On some types of optimization problems in complex space. (English) Math., Rev. Anal. Numér. Théor. Approximation, Anal. Numér. Théor. Approximation 10, 11-16 (1981), Zbl 0474.90071.

Duca, Dorel I., Linear optimality criteria in nonlinear programming in complex space. (English) Stud. Univ. Babes-Bolyai, Math. 26, No.3, 73-79 (1981), Zbl 0474.90070.

Duca, Dore, I., Asupra unui rezultat din teoria dualităţii în programarea matematică în domeniul complex, Lucrările seminarului itinerant de ecuaţii funcţionale, aproximare şi convexitate (Cluj-Napoca, decembrie 1981), 119-126, Univ. Babeş-Bolyai, Cluj-Napoca, 1981.

Duca, Dorel I., Mathematical programming in complex space, Doctoral thesis, Unviersity of Cluj-Napoca, Cluj-Napoca, 1981.

(2,1)-order duality in nonlinear programming in complex space, Lucrările seminarului "Th. Angheluţă" (Cluj-Napoca, iunie 1983), 99-104, Preprint, Institutul Polithenic din Cluj-Napoca, Cluj-Napoca, 1983.

Duca, Dorel I., Efficiency criteria in vectorial programming in complex space. (English) Prepr., "Babes-Bolyai" Univ., Fac. Math., Res. Semin. 2, 51-54 (1983), Zbl 0529.90084.

Duca, Dore I., On duality in nonlinear programming in complex space, Itinerant seminar on functional equations, approximation and convexity (Cluj-Napoca, 1984), 45-48, Preprint, 84-6, Univ. "Babeş-Bolyai", Cluj-Napoca, 1984.

Duca, Dorel I., Efficiency criteria in vectorial programming in complex space without convexity. (English)Cah. Cent. Étud. Rech. Opér. 26, 217-226 (1984), Zbl 0552.90086.

Duca, Dorel I., Duality in mathematical programming in complex space. Converse theorems. (English) Math., Rev. Anal. Numér. Théor. Approximation, Anal. Numér. Théor. Approximation 13, 15-22 (1984), Zbl 0551.49013.

Duca, Dorel I., Second-order duality in nonlinear programming in complex space. (English) Approximation and optimization, Proc. Colloq., Cluj-Napoca/Rom. 1984, 213-222 (1985), Zbl 0579.49012.

Duca, Dore I., On the higher-order duality in nonlinear programming in complex space, Seminar on optimization theory (Cluj-Napoca, 1985), 39-50, Preprint, 85-5, Univ. "Babeş-Bolyai", Cluj-Napoca, 1985.

Duca, Dorel I., Vectorial programming in complex space. (English) Rep., "Babes-Bolyai" Univ., Fac. Math., Res. Sémin. 8, 3-82 (1986), Zbl 0651.90081.

Duca, Dorel I., The dual of the dual in mathematical programming in complex space (to appear).

Duca, Dorel I., On the Farkas type theorem for complex linear equations and inequalities (to appear).

Duca, Dore I., Saddlepoint necessary condition of nonlinear programming in complex space (to appear).

Duca, Dore I., Theorem of Motzkin's alternative for nonhomogeneous complex linear equations and inequalities (to appear).

Duca, Dore I., On theorems of the alternative for nonhomogeneous complex linear equations and inequalities (to appear).

Duca, Eugenia and Duca, Dorel I., Asupra structuii mulţimii punctelor eficiente într-o problemă de programare vectorială în domeniul complex. Lucrările seminarului itinerant de ecuaţii funcţionale, aproximare şi convexitate (Cluj-Napoca, mai 1979), 41-47, Preprint, Univ. "Babeş-Bolyai", Cluj-Napoca, 1979.

Ferrero, O., On non-linear programming in complex space, Paper No. 124, Dipartimento di matematica, Università di Pisa, Italy, 1985.

Gulati, T.R., Duality for nondifferentiable fractional programming in complex space, Paper presented at the 6th Annual Convention of O.R. Society of India, New Delhi (1973), Abstract published in Opsearch, 10(1973), no. 3-4, 221.

Gulati, T.R., A Fritz John type sufficient optimality theorem in complex space. (English) Bull. Aust. Math. Soc. 11, 219-224 (1974), Zbl 0283.90046, https://doi.org/10.1017/s0004972700043811

Gulati, T.R., Optimality criteria and duality in complex fractional and indefinite programming, Ph. D. Thesis, I.I.T., New Delhi, 1975.

Gulati, T.R., On nonlinear nondifferentiable complex programming problems. (English) Z. Angew. Math. Mech. 62, 418-420 (1982), Zbl 0503.90083, https://doi.org/10.1002/zamm.19820620816

Gulati, T.R., Chandra, Suresh, A duality theorem for complex fractional programming. (English) Z. angew. Math. Mech. 55, 348-349 (1975), Zbl 0314.90092, https://doi.org/10.1002/zamm.19750550609

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Gupta, Bina, Duality and existence relations for a pair of linear multiple-objective programs in complex space. (English) Math. Jap. 27, 5-15 (1982), Zbl 0476.90072.

Gupta, Bina, Existence and duality relations for multi-objective programs in complex space. (English), Opsearch 19, 178-182 (1982), Zbl 0506.90080.

Gupta, Bina, Second order duality and symmetric duality for nonlinear programs in complex space. (English) J. Math. Anal. Appl. 97, 56-64 (1983), Zbl 0524.90078, https://doi.org/10.1016/0022-247x(83)90237-8

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Hanna, M.T. and Simaan, M., A closed-form solution to a quadratic programming problem in complex variables. Proceedings of the 23rd I.E.E.E. Conference on Decision and Control (Cat. No., 84 CH 2093-3), Las Vegas, NV, USA, 12-14 Dec. 1984), Vol. 2, pp. 1987-1092, IEEE, New York, USA, 1984, https://doi.org/10.1109/cdc.1984.272180

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Kirievskii, L. A., Duality in complex mathematical programming, Proceedings of the Fourth Winter School on Mathematical Programming and Related Questions (Drogobych, January 25-February 6, 1971, No. 2), 32-44, Moscow, Inz-Stroitel, Inst., Moscow, 1971.

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Mahajan, G.D. and Vartak, M. N., Symmetry and duality for a class of nonlinear programs in complex space, J. Indian Statist. Assoc., 14 (1976), no. 1, 52-64.

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Mond, B. and Greenblatt, Z., A note on duality for complex linear programming, Opsearch, 12(1975), no. 3-4, 119-123.

Mond, B. and Hanson, M. A., Symmetric duality for quadratic programming in complex space, J. Math. Anal. Appl., 23(1968), no. 2, 284-293, https://doi.org/10.1016/0022-247x(68)90068-1

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1988-08-01

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Duca, D. I., & Stancu-Minasian, I. M. (1988). Mathematical programming in complex space: a comprehensive bibliography. Anal. Numér. Théor. Approx., 17(2), 133–140. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1988-vol17-no2-art5

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Vol. 17 No. 2 (1988)

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