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Semiinfinite multiobjective fractional programming. Part I: Sufficient efficiency conditions

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we formulate and discuss a fairly large number of sets of global parametric sufficient efficiency criteria under various generalized (η, ρ)-invexity assumptions, and prove a semiinfinite version of a well-known second-order sufficiency result for a semiinfinite multiobjective fractional programming problem.
Wydawca
Rocznik
Strony
199--224
Opis fizyczny
Bibliogr. 35 poz.
Twórcy
autor
autor
  • Department of Mathematics and Computer Science, Northern Michigan University, Marquette, MI 49855, USA, gzalmai@nmu.edu
Bibliografia
  • [1] I. Ahmad and Z. Husain, Second order (F, alpha, rho, d)-convexity and duality in multiobjective programming. Inform. Sci. 176 (2006), 3094-3103.
  • [2] A. Ben-Israel and B. Mond, What is invexity?, J. Austral. Math. Soc. Series B 28 (1986), 1-9.
  • [3] D. Bhalia and P. Jain, Generalized (F, rho)-convexity and duality for nonsmooth multiobjective programs, Optimization 31 (1994), 153-164.
  • [4] E. Caprari, eta-invex functions and (F, rho)-convex functions: properties and equivalences, Optimization 52 (2003), 65-74.
  • [5] A. Chinchuluun. D. Yuan, and P. M. Pardalos. Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity, Ann.Oper. Res. 154(2007), 133-147.
  • [6] B. D. Craven, Invex functions and constrained local minima. Bull. Austral. Math. Soc. 24(1981), 357-366.
  • [7] W. Dinkelbach, On nonlinear fractional programming. Management Sci. 13 (1967), 492-498.
  • [8] A. V. Fiacco and G. P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, SI AM, Philadelphia, 1990.
  • [9] G. Giorgi and A. Guerraggio, Various types of nonsmooth invex functions, J. Inform. Optim. Sci. 17(1996), 137-150.
  • [10] G. Giorgi and S. Mititelu. Convexites generatisees et proprietes. Revue Roumaine Math. Pures Appl. 38(1993), 125-172.
  • [11] M. A. Hanson, On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl. 80 (1981), 545-550.
  • [12] M. A. Hanson and B. Mond, Further generalizations of convexity in mathematical programming, J. Inform. Optim. Sci. 3 (1982), 25-32.
  • [13] V. Jeyakumar, Strong and weak invexity in mathematical programming. Methods Open Res. 55 (1985), 109-125.
  • [14] P. Kanniappan and P. Pandian, On generalized convex functions in optimization theory - A survey, Opsearch 33 (1996), 174-185.
  • [15] Z. A. Liang and Z. W. Shi, Optimality conditions and duality for a minimax fractional programming problem with generalized convexity, J. Math. Anal. Appl. 277 (2003), 474-^88.
  • [16] D. H. Martin, The essence of invexity, J. Optim. Theory Appl. 47 (1985), 65-76.
  • [17] K. M. Miettinen, Nonlinear Multiobjective Optimization, Kluwer Academic Publishers, Boston, 1999.
  • [18] S. Mititelu and I. M. Stancu-Minasian, Invexity at a point: Generalizations and classification. Bull. Austral. Math. Soc. 48, 117-126.
  • [19] B. Mond, and T. Weir, Generalized concavity and duality. Generalized Concavity in Optimization and Economics (S. Schaible and W. T. Ziemba, eds.). Academic Press, New York, 1981, pp. 263-279.
  • [20] R. Pini, Invexity and generalized convexity. Optimization 22 (1991), 513-525.
  • [21] R. Pini, and C. Singh, A survey of recent [1985-1995] advances in generalized convexity with applications to duality theory and optimality conditions. Optimization 39 (1997), 311-360.
  • [22] T. W. Reiland, Nonsmooth invexity. Bull. Austral. Math. Soc. 42 (1990), 437-446.
  • [23] Y. Sawaragi, H. Nakayama, and T. Tanino, Theory of Multiobjective Optimization, Academic Press, New York, 1986.
  • [24] D. J. White, Optimality and Efficiency, Wiley, New York, 1982.
  • [25] P. L. Yu, Multiple-Criteria Decision Making: Concepts, Techniques, and Extensions, Plenum Press, New York, 1985.
  • [26] D. H. Yuan, X. L. Liu, A. Chinchuluun, and P. M. Pardalos, Nondifferentiable minimax fractional programming problems with (C, alpha , rho, d)-convexity, J. Optim. Theory Appl. 129 (2006), 185-199.
  • [27] G. J. Zalmai, Proper efficiency conditions and duality models for nonsmooth multiobjective fractional programming problems with operator constraints, part I: Theory, Util. Math. 50 (1996), 163-201.
  • [28] G. J. Zalmai, Proper efficiency conditions and duality models for nonsmooth multi-objective fractional programming problems with operator constraints, part II: Applications, Util. Math. 51 (1997), 193-237.
  • [29] G. J. Zalmai, Proper efficiency principles and duality models for a class of continuous-time multiobjective fractional programming problems with operator constraints, J. Stat. Manag. Syst. 1 (1998), 11-59.
  • [30] G. J. Zalmai, Efficiency conditions and duality models for multiobjective fractional subset programming problems with generalized (digamma, alpha, rho, theta)-V-convex functions, Comput. Math. Appl. 43 (2002), 1489-1520.
  • [31] G. J. Zalmai and Q. Zhang, Global nonparametric sufficient optimality conditions for semiinfinite discrete minmax fractional programming problems involving generalized (eta, rho)-invex functions, Numer. Funct. Anal. Optim. 28 (2007), 173-209.
  • [32] G. J. Zalmai and Qinghong Zhang, Generalized (digamma, beta, phi, rho, theta)-univex functions and global parametric sufficient optimality conditions in semiinfinite discrete minmax fractional programming, PanAmerican J. Math. 17 (2007), 1-26.
  • [33] G. J. Zalmai and Qinghong Zhang, Generalized (digamma, beta, phi, rho, theta)-univexfunctions and parametric duality models in semiinfinite discrete minmax fractional programming. Advances Nonlin. Var. Ineq. 10 (2007), 21-42. 17 (2007), 1-26.
  • [34] G. J. Zalmai and Q. Zhang, Global semiparametric sufficient efficiency conditions for semiinfinite multiobjective fractional programming problems involving generalized (alpha, eta, rho)-V-invexfunctions. Southeast Asian Bull. Math. 32 (2008), 573-599.
  • [35] G. J. Zalmai and Q. Zhang, Semiinfinite multiobjective fractional programming. Part II: Duality models. Journal of Applied Analysis (forthcoming).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD7-0033-0003
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