THE SUFFICIENT EFFICIENCY CONDITIONS IN SEMIINFINITE MULTIOBJECTIVE FRACTIONAL PROGRAMMING UNDER HIGHER ORDER EXPONENTIAL TYPE HYBRID TYPE INVEXITIES

摘要/Abstract

摘要：

First, a class of higher order exponential type hybrid (α, β, γ, η, ρ, h(·,·), κ(·,·), ω(·,·,·), ω(·,·,·), θ)-invexities is introduced, second, some parametrically sufficient efficiency conditions based on the higher order exponential type hybrid invexities are established, and finally some parametrically sufficient efficiency results under the higher order exponential type hybrid (α, β, γ, η, ρ, h(·,·), κ(·,·), ω(·,·,·), ω(·,·,·), θ)-invexities are investigated to the context of solving semiinfinite multiobjective fractional programming problems. The notions of the higher order exponential type hybrid (α, β, γ, η, ρ, h(·,·), κ(·,·), ω(·,·,·), ω(·,·,·), θ)-invexities encompass most of the generalized invexities in the literature. To the best of our knowledge, the results on semiinfinite multiobjective fractional programming problems established in this communication are new and application-oriented toward multitime multiobjectve problems as well as multiobjective control problems.

关键词: semiinfinite fractional programming, multiobjective fractional programming, Hanson-Antczak-type generalized HA(α, β, γ, η, ρ, θ)-V-invex functions

Abstract:

中图分类号:

90C29

Ram U. VERMA. THE SUFFICIENT EFFICIENCY CONDITIONS IN SEMIINFINITE MULTIOBJECTIVE FRACTIONAL PROGRAMMING UNDER HIGHER ORDER EXPONENTIAL TYPE HYBRID TYPE INVEXITIES[J]. 数学物理学报(英文版), 2015, 35(6): 1437-1453.

Ram U. VERMA. THE SUFFICIENT EFFICIENCY CONDITIONS IN SEMIINFINITE MULTIOBJECTIVE FRACTIONAL PROGRAMMING UNDER HIGHER ORDER EXPONENTIAL TYPE HYBRID TYPE INVEXITIES[J]. Acta mathematica scientia,Series B, 2015, 35(6): 1437-1453.

参考文献

[1] Antczak T. The notion of V-r-invexity in differentiable multiobjective programming. J Appl Anal, 2005, 11: 63-79
[2] Antczak T. Optimality and duality for nonsmooth multiobjective programming problems with V-r-invexity. J Global Optim, 2009, 45: 319-334
[3] Ben-Israel A, Mond B. What is invexity? J Austral Math Soc Ser B, 1986, 28: 1-9
[4] Bhatia D, Kumar P. Multiobjective control problem with generalized invexity. J Math Anal Appl, 1995, 189: 676-692
[5] Chen H, Hu C F. On the resolution of the Vasicek-type interest rate model. Optimization, 2009, 58: 809-822
[6] Craven B D. Invex functions and constrained local minima. Bull Austral Math Soc, 1981, 24: 357-366
[7] Daum S, Werner R. A novel feasible discretization method for linear semi-infinite programming applied to basket option pricing. Optimization, 2011, 60: 1379-1398
[8] Ergenç T, Pickl S W, Radde N, Weber G -W. Generalized semi-infinite optimization and anticipatory systems. Int J Comput Anticipatory Syst, 2004, 15: 3-30
[9] Fiacco A V, Kortanek K O, eds. Semi-infinite Programming and Applications. Lecture Notes in Economics and Mathematical Systems, Vol 215. Berlin: Springer, 1983
[10] Giorgi G, Guerraggio A. Various types of nonsmooth invex functions. J Inform Optim Sci, 1996, 17: 137-150
[11] Giorgi G, Mititelu ?t. Convexités généralisées et propriétés. Rev Roumaine Math Pures Appl, 1993, 38: 125-172
[12] Glashoff K, Gustafson S A. Linear Optimization and Approximation. Berlin: Springer, 1983
[13] Goberna M A, López M A. Linear Semi-Infinite Optimization. New York: Wiley, 1998
[14] Goberna M A, López M A, eds. Semi-infinite Programming - Recent Advances. Dordrecht: Kluwer, 2001
[15] Gribik P R. Selected applications of semi-infinite programming//Coffman C V, Fix G J, eds. Constructive Approaches to Mathematical Models. New York: Academic Press, 1979: 171-187
[16] Gustafson S A, Kortanek K O. Semi-infinite programming and applications//Bachem A, et al, eds. Mathematical Programming: The State of the Art. Berlin: Springer, 1983: 132-157
[17] Hanson M A. On sufficiency of the Kuhn-Tucker conditions. J Math Anal Appl, 1981, 80: 545-550
[18] Hanson M A, Mond B. Further generalizations of convexity in mathematical programming. J Inform Optim Sci, 1982, 3: 25-32
[19] Henn R, Kischka P. Über einige Anwendungen der semi-infiniten Optimierung. Zeitschrift Oper Res, 1976, 20: 39-58
[20] Hettich R, ed. Semi-infinite Programming, Lecture Notes in Control and Information Sciences, Vol 7. Berlin: Springer, 1976
[21] Hettich R, Kortanek K O. Semi-infinite programming: theory, methods, and applications. SIAM Review, 1993, 35: 380-429
[22] Hettich R, Zencke P. Numerische Methoden der Approximation und Semi-infinite Optimierung. Stuttgart: Teubner, 1982
[23] Jess A, Jongen H Th, Nerali?, Stein O. A semi-infinite programming model in data envelopment analysis. Optimization, 2001, 49: 369-385
[24] Jeyakumar V, Mond B. On generalised convex mathematical programming. J Austral Math Soc Ser B, 1992, 34: 43-53
[25] Kanniappan P, Pandian P. On generalized convex functions in optimization theory - A survey. Opsearch, 1996, 33: 174-185
[26] López M, Still G. Semi-infinite programming. European J Oper Res, 2007, 180: 491-518
[27] Martin D H. The essence of invexity. J Optim Theory Appl, 1985, 47: 65-76
[28] Miettinen K M. Nonlinear Multiobjective Optimization. Boston: Kluwer Academic Publishers, 1999
[29] Mititelu ?t. Invex functions. Rev Roumaine Math Pures Appl, 2004, 49: 529-544
[30] Mititelu ?t. Invex sets and nonsmooth invex functions. Rev Roumaine Math Pures Appl, 2007, 52: 665-672
[31] Mititelu ?t, Postolachi M. Nonsmooth invex functions via upper directional derivative of Dini. J Adv Math Stud, 2011, 4: 57-76
[32] Mond B, Smart I. Duality and sufficiency in control problems with invexity. J Math Anal Appl, 1988, 136: 325-333
[33] Mond B, Weir T. Generalized concavity and duality//Schaible S, Ziemba W T, eds. Generalized Concavity in Optimization and Economics. New York: Academic Press, 1981: 263-279
[34] Nerali? L, Stein O. On regular and parametric data envelopment analysis. Math Methods Oper Res, 2004, 60: 15-28
[35] Pitea A, Postolache M. Duality theorems for a new class of multitime multiobjective variational problems. J Global Optimization, 2012, 54(1): 47-58
[36] Pitea A, Postolache M. Minimization of vectors of curvilinear functionals on the second order jet bundle: Necessary conditions. Optimization Letters, 2012, 6(3): 459-470
[37] Pitea A, Postolache M. Minimization of vectors of curvilinear functionals on the second order jet bundle: Sufficient efficiency conditions. Optimization Letters, 2012, 6(8): 1657-1669
[38] Sawaragi Y, Nakayama H, Tanino T. Theory of Multiobjective Optimization. New York: Academic Press, 1986
[39] Stein O. Bilevel Strategies in Semi-infinite Programming. Boston: Kluwer, 2003
[40] Verma R U. Weak ε-efficiency conditions for multiobjective fractional programming. Appl Math Comput, 2013, 219: 6819-6827
[41] Verma R U. Second-order (Φ, η, ρ, θ)-invexities and parameter-free ε-efficiency conditions for multiobjective discrete minmax fractional programming problems. Adv Nonlinear Variational Inequalities, 2014, 17(1): 27-46
[42] Verma R U. New ε-optimality conditions for multiobjective fractional subset programming problems. Trans Math Prog Appl, 2013, 1(1): 69-89
[43] Verma R U. Parametric duality models for multiobjective fractional programming based on new generation hybrid invexities. J Appl Funct Anal, 2015, 10(3/4): 234-253