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

Abrams, R. A., Nonlinear programming in complex space, Doctoral thesis in applied-mathematics, Northwestern Univ., Evanston, Illinois, 1969.

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

Ben-Israel, Adi, Theorems of the alternative for complex linear inequalities, Israel J.. Math., 7, 1969, no. 2, 129-136, https://doi.org/10.1007/bf02771659

Ben-Israel, Adi, Theorems of the alternative for complex linear inequalities, Israel J.. Math., 7, 1969, no. 3, 293.

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

Gulati, T.R. ,Chandra, Suresh, A note on symmetric dual quadratic programs in real and complex spaces. (English) Cah. Cent. Étud. Rech. Opér. 21, 77-80 (1979), Zbl 0408.90062.

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

Gupta, R.P., Symmetric dual and self dual nonlinear programs in complex space, Department of Mathematics, I.I.T., Kanpur, India, 1969.

Gupta, R.P., Self dual quadratic program in complex space. (English) Ganita 20, No.2, 93-99 (1969), Zbl 0221.90039.

Gupta, R.P., Duality theorem for convex program in complex space. (English) Cah. Cent. Étud. Rech. Opér. 12, 95-102 (1970), Zbl 0282.90036.

Gupta, R.P., Symmetric dual quadratic program in complex space. (English) Proc. Indian Acad. Sci., Sect. A 72, 74-87 (1970), Zbl 0221.90040, https://doi.org/10.1007/bf03050408

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

Hanna, M.T., Simaan, M., A closed-form solution to a quadratic programming problem in complex variables. (English) Optimization Theory Appl. 47, 437-450 (1985), Zbl 0556.90064J, https://doi.org/10.1007/bf00942190

Hanson, M.A., Mond, B., Quadratic programming in complex space. (English) J. Math. Anal. Appl. 20, 507-514 (1967), Zbl 0157.50001, https://doi.org/10.1016/0022-247x(67)90076-5

Hanson, M.A., Mond, B., Duality for nonlinear programming in complex space. (English) J. Math. Anal. Appl. 28, 52-58 (1969), Zbl 0191.48901, https://doi.org/10.1016/0022-247x(69)90107-3

Jain, O.P., Duality for fractional functional programming, Cahiers Centre Études Rech. Opér., 21(1979), no. 1, 81-86.

Jain, O.P., Saxena, P.C., A duality theorem for a special class of programming problems in complex space. (English) J. Optimization Theory Appl. 16, 207-220 (1975), Zbl 0283.90041, https://doi.org/10.1007/bf01262933

Jain, O.P,; Saxena, P.C., Symetric and self duality for a class of non-linear programming problems in complex space. (English) Port. Math. 37, 55-72 (1978), Zbl 0456.90072.

Kaul, R.N., On Eisenberg's theorem in complex space, Ann. Conf. Indian Math. Soc., Gorankhpur, Dec., 1970.

Kaul, R. N., On linear inequalities in complex space, Amer. Math. Monthly, 77(1970), no. 9, 956-960, https://doi.org/10.1080/00029890.1970.11992637

Kaul, R. N., Duality theorems for nonlinear programming in complex space, Ann. Conf. Indian Math. Soc., Gorankhpur, Dec., 1970.

Kaul, R.N., Symmetric dual nonlinear programs in complex space. (English) J. Math. Anal. Appl. 33, 140-148 (1971), Zbl 0209.51401, https://doi.org/10.1016/0022-247x(71)90188-0

Kaul, R.N., A note on duality theorem for complex programming. (English) Math. Student 41, 48-50 (1973), Zbl 0362.90055.

Kaul, R.N., Datta, Neelam, On equivalence between a saddle-point problem and linear programming in complex space. (English) Z. Angew. Math. Mech. 59, 133-135 (1979), Zbl 0412.90067, https://doi.org/10.1002/zamm.19790590212

Kaul, R.N., Gupta, B., Multi-objective programming in complex space. (English) Z. Angew. Math. Mech. 61, 599-601 (1981), Zbl 0472.90057, https://doi.org/10.1002/zamm.19810611110

Kaul, R.N., Rani, Oma, A theorem of Fritz John in complex programming. (English) Linear Algebra Appl. 7, 217-232 (1973)., Zbl 0266.90056, https://doi.org/10.1016/0024-3795(73)90041-4

Kaul, R.N., Rani, O., Symmetric-duality for nonlinear programming in complex space. (English) Z. angew. Math. Mech. 53, 483-484 (1973), Zbl 0263.90033, https://doi.org/10.1002/zamm.19730530707

Kaul, R. N. and Sharma, sudesh, General symmetric dual programs in complex space, Opsearch, 7(1970), no. 2, 176-174.

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.

Kushimoto, Shigeru, Converse duality theorem for pseudo-convex programming in complex space. (English) Math. Jap. 18, 79-86 (1973), Zbl 0283.90047.

Kushimoto, Shigeru, Pseudo-convex programming in complex space. (English) Math. Jap. 19, 177-182 (1974), Zbl 0316.90072.

Kushimoto, Shigeru, Self-duality for mathematical programming in complex space. (English) Sci. Rep. Niigata Univ., Ser. A 11, 13-20 (1974), Zbl 0359.90065.

Kushimoto, Shigeru, Duality for quadratic programs in complex space. (English) Math. Jap. 20(1975), 285-292 (1976), Zbl 0332.90034.

Kushimoto, S., Positive definite programming in complex space, Math. Japon., 21(1976), no. 3, 303-309.

Levinson, N., Linear programming in complex space, J. Math. Anal. Appl., 14(1966), no. 1, 44-62, https://doi.org/10.1016/0022-247x(66)90061-8

Mahajan, D.G. and Vartak, M. N., Generalized of some nonlinear programming problems in complex space, J. Indian Statist. Assoc. 14(1976), no.,1, 39-51.

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.

Mahajan, D.G., Vartak, M.N., Duality for generalized problems in complex programming. (English) Bull. Aust. Math. Soc. 14, 11-22 (1976), Zbl 0333.90040, https://doi.org/10.1017/s0004972700024825

Marusciac, I., Infrapolynomials and Pareto optimization. (English) Math., Rev. Anal. Numér. Théor. Approximation, Math. 22(45), 297-307 (1980), Zbl 0496.90071.

Marusciac, I., Infrapolynomials and Pareto optimization. Rev. Roum. Math. Pures Appl. 26, 437-448 (1981), Zbl 0465.30008.

McCallum, Ch. J. Jr., the linear complementarity problem in complex space, Bull. Op. Res. Soc. am. (USA), Vol. 19, Supp. 1, 1971, (39th National Meeting of the Operations Research Societyu of America, Dallas, Tex., 5-7 May, 1971), Also as: Report TR-70-12 (AD-712769), Stanford Univ., Calif., USA (Aug. 1970), 119 p.

McCallum, Ch. J. Jr., Existence theory for complex linear complementarity problem, J. Math. Anal. Appl. 40(1972), no. 3, 738-762, https://doi.org/10.1016/0022-247x(72)90017-0

McCallum, Ch. J. Jr., Solution of the complex linear complementarity problem, J. Math. Anal. Appl., 44(1973), no. 3, 643-660, https://doi.org/10.1016/0022-247x(73)90007-3

Mikolajczyk, L., Mathematical programming in complex domain. (Polish) Zesz. Nauk. Politech. Rzeszowskiej, Folia Sci. Univ. Tech. Resoviensis 16, Mat. Fiz. 2, 97-111 (1984), Zbl 0588.90077.

Mishra, B.K., Das, C., A note on sufficiency theorem in complex space. (English) Math. Jap. 26, 139-144 (1981), Zbl 0466.90064.

Mond, Bertram, Nonlinear nondifferentiable programming in complex space. (English) Nonlinear Programming, Proc. Sympos. Math. Res. Center, Univ. Wisconsin, Madison 1970, 385-400 (1970), Zbl 0244.90038, https://doi.org/10.1016/b978-0-12-597050-1.50017-8

Mond, B., An extension of the transposition theorems of Farkas and Eisenberg. (English) J. Math. Anal. Appl. 32, 559-566 (1970), Zbl 0208.21802, https://doi.org/10.1016/0022-247x(70)90277-5

Mond, Bertram, On the complex complementarity problem. (English)Bull. Aust. Math. Soc. 9, 249-257 (1973), Zbl 0294.90067, https://doi.org/10.1017/s0004972700043148

Mond, B., Nonlinear complex programming. (English) J. Math. Anal. Appl. 43, 633-641 (1973), Zbl 0291.90066, https://doi.org/10.1016/0022-247x(73)90282-5

Mond, B., duality for complex nonlinear program. Opsearch, 11(1974), no.1, 1-9.

Mond, B., Duality for complex nonlinear programs. Opsearch, 11(1974), no. 2, 90-99.

Mond, Bertram, Duality for complex programming. (English) J. Math. Anal. Appl. 46, 478-486 (1974), Zbl 0281.90062, https://doi.org/10.1016/0022-247x(74)90254-6

Mond, B., Symmetric duality for nonlinear programming, Opsearch, 13(1976), no. 1, 1-10.

Mond, B., Craven, B.D., A class of nondifferentiable complex programming problems. (English) Math. Operationsforsch. Stat. 6, 581-591 (1975), Zbl 0337.90061, https://doi.org/10.1080/02331887508801238

Mond, B., Craven, B.D., Sufficient optimality conditions for complex programming with quasi- concave constraints. (English) Math. Operationsforsch. Stat., Ser. Optimization 8, 445-453 (1977), Zbl 0381.90087, https://doi.org/10.1080/02331937708842441

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

Mond, B., Hanson, M.A., On duality for real and complex programming problems. (English) J. Math. Anal. Appl. 24, 307-312 (1968), Zbl 0213.44603, https://doi.org/10.1016/0022-247x(68)90032-2

Mond, B., Hanson, M.A., A complex transposition theorem with applications to complex programming. (English) Linear Algebra Appl. 2, 49-56 (1969), Zbl 0181.04002, https://doi.org/10.1016/0024-3795(69)90006-8

Mond, B., Hanson, M.A., Some generalizations and applications of a comples transposition theorem. (English) Linear Algebra Appl. 2, 401-411 (1969), Zbl 0184.05705, https://doi.org/10.1016/0024-3795(69)90013-5

Mond, B. and Murray, G. J., Game theory in complex space, Pure Mathematics Research Paper No. 79-12, August, 1979, Department of mathematics, La Trobe University, Melbourne, Australia.

Mond, B., Murray, G.J., Game theory in complex space. (English) Opsearch 19, 1-11 (1982), Zbl 0484.90095.

Mond, B., Murray, G.J., A minimax theorem for matrix games in complex space. (English) Opsearch 20, 25-34 (1983), Zbl 0503.90094.

Mond, B., Murray, G.J., On solving complex programs. (English) Opsearch 21, 262-270 (1984), Zbl 0559.90065.

Mond, B., Parida, J., On solvability of the complex linear complementarity problem. (English) Indian J. Pure Appl. Math. 15, 962-967 (1984), Zbl 0557.90101.

Nanda, Sribatsa, Nanda, Sudarsan, A complex nonlinear complementarity problem. (English) Bull. Aust. Math. Soc. 19, 437-444 (1978), Zbl 0417.90084, https://doi.org/10.1017/s0004972700008960

Nikonov, V.A., Applciation of a theorem of the alternative to nonlinear programming in a complex space (Russian), Applciation of computers to the solution of problems in mathematical physics and automatic control systems (A.N. Čekalin and E. V. Ermolin eds.), Univ. Kazan, Kazan, 1978, 54-61.

Nikonov, V. A., Stability in nonlinear complex programming (Russian), Applicaiton of computers to the solution of problems in mathematical physics and automatic control systems (A. N. Čekalin and E. V. Ermolin eds.), Univ. Kazan, Kazan, 1978, 61-64.

Parida, J., A note on the duality theorems of linear programming in complex space. (English) Z. angew. Math. Mech. 55, 772-774 (1975), Zbl 0323.90029, https://doi.org/10.1002/zamm.19750551219

Parida, J., On converse duality in complex nonlinear programming. (English) Bull. Aust. Math. Soc. 13, 421-427 (1975), Zbl 0318.90051, https://doi.org/10.1017/s0004972700024667

Parida, J., Self-duality in complex mathematical programming. (English) Cah. Cent. Étud. Rech. Opér. 20, 95-101 (1978), Zbl 0383.90087.

Parida, J., Nayak, K.C., An existence theorem for the complex linear complementarity problem. (English) Z. Angew. Math. Mech. 59, 275-276 (1979), Zbl 0414.90088, https://doi.org/10.1002/zamm.19790590613

Parida, J., Sahoo, B., On the complex nonlinear complementary problem. (English) Bull. Aust. Math. Soc. 14, 129-136 (1976), Zbl 0329.90063, https://doi.org/10.1017/s0004972700024898

Parida, J., Sahoo, B., Existence theory for the complex nonlinear complementarity problem. (English) Bull. Aust. Math. Soc. 14, 417-423 (1976), Zbl 0323.90040, https://doi.org/10.1017/s0004972700025338

Parida, J., Sahoo, B., On an application of the complex nonlinear complementarity problem. (English) Bull. Aust. Math. Soc. 15, 141-148 (1976), Zbl 0329.90064, https://doi.org/10.1017/s0004972700036868

Parida, J., Sahoo, B., Existence theory for symmetric dual nonlinear programs in complex space. (English) Z. angew. Math. Mech. 58, 51-53 (1978), Zbl 0383.90089, https://doi.org/10.1002/zamm.19780580109

Parkash, O., Saxena, P.C., Patkar, V., Nondifferentiable fractional programming in complex space. (English) Z. Angew. Math. Mech. 64, 59-62 (1984), Zbl 0537.90089, https://doi.org/10.1002/zamm.19840640110

Rani, O., A duality theorem for complex nonlinear programming, Opsearch, 10(1973), no. 1, 14-23.

Rani, Oma, Kaul, R.N., Nonlinear programming in complex space. (English) J. Math. Anal. Appl. 43, 1-14 (1973), Zbl 0265.90049, https://doi.org/10.1016/0022-247x(73)90252-7

Rani, O. and Kaul, R. N., General symmetric dual quadratic programs in complex space, Z. Oper. Res. A-B, 17(1973), no. 1, 5-12, https://doi.org/10.1007/bf01951365

Rani, Oma, Lata, Manju, On a class of symmetric non-linear programming problems in complex space. (English) Z. angew. Math. Mech. 55, 343-345 (1975), Zbl 0313.90054, https://doi.org/10.1002/zamm.19750550607

Rani, O. and Lata, Manju, Symmetric and solf-dual non-linear programs in complex space. Trabajos Estudiest. Invest. Operat. (to appear).

Sahoo, B., Parida, J., A note on converse duality in complex nonlinear programming. (English)Z. angew. Math. Mech. 57, 491 (1977), Zbl 0369.90106, https://doi.org/10.1002/zamm.19770570811

Saxena, P.C., Duality theorem for fractional functional programming in complex space. (English) Port. Math. 37, 87-92 (1978), Zbl 0463.90089.

Saxena, P.C., Patkar, Vivek, Linear fractional functional programming in complex space. (English) Port. Math. 37, 73-80 (1978), Zbl 0464.90076.

Saxena, P.C. and Patkar, V., Non-linear non-differentiable fraction programming in complex space, Cahiers Centre Études rech. Opér., 20(1978), no. 2, 183-193.

Saxena, P.C., Patkar, V. and Parkash, O., Linear fractional functional programming in complex space, Z. Angew. Math. Mech., 59(1979), no. 6, 276-278, https://doi.org/10.1002/zamm.19790590614

Scott, C.H. and Jefferson, T.R., Duality in finite dimensional complex space, Bull. Austral. Math. Soc., 18(1978), no. 1, 65-75, https://doi.org/10.1017/s0004972700007814

Sharma, Sudesh, Kaul, R.N., Symmetric and self-dual quadratic programs. (English) Opsearch 5(1968), 157-164 (1970), Zbl 0249.90056.

Sinha, S.M., Jain, O.P., Symmetry and self-duality in nonlinear programming. (English) Cah. Cent. Étud. Rech. Opér. 18, 355-366 (1976), Zbl 0346.90040.

Smiley, M.F., Duality in complex homogeneous programming. (English) J. Math. Anal. Appl. 40, 153-158 (1972), Zbl 0237.90055, https://doi.org/10.1016/0022-247x(72)90038-8

Stancu-Minasian, I.M., Fractional programming in complex space: the state of the art, Revue Roumaine de Mathématique Pures et Appliquée, 26(1981), no. 3, 481-491.

Stancu-Minasian, I.M., Duca, Dorel I., Nishida, Toshio, Multiple objective linear fractional optimization in complex space. (English) Math. Jap. 35, No.1, 195-203 (1990), Zbl 0694.90090.

Swarup, K., Sharma, I.C., Programming with linear fractional functionals in complex space. (English) Cah. Cent. Étud. Rech. Opér. 12, 103-109 (1970), Zbl 0208.46501.

Tanimoto, T., Optimization by a method of maximum slope in the complex plane and its application to the transportation problem. (English) Rend. Sem. Mat. Univ. Padova 48(1972), 365-376 (1973), Zbl 0277.90080.

Weir, T., Mond, B., Generalized convexity and duality for complex programming problems. (English) Cah. Cent. Étud. Rech. Opér. 26, 137-142 (1984), Zbl 0538.90071.

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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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