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Parametric duality Models for Semi-infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η,ρ)-Invex Functions

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Acta Mathematicae Applicatae Sinica 2007年第3期23卷 353-376页

作者： G.J.Zalmai Department of Mathematics and Computer Science Northern Michigan UniversityMarquetteMichigan 49855USA

A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.

关键词： Semi-infinite programming discrete minmax fractional programming generalized invex functions,infinitely many equality and inequality constraints parametric duality models duality theorems

Parametric duality Models for Semiinfinite Multiobjective Fractional Programming Problems Containing Generalized (α, η, ρ)-V-Invex Functions

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Acta Mathematicae Applicatae Sinica 2013年第2期29卷 225-240页

作者： G.J. ZALMAI Qing-hong ZHANG Department of Mathematics and Computer Science Northern Michigan University

In this paper, we present several parametric duality results under various generalized （a,v,p）-V- invexity assumptions for a semiinfinite multiobjective fractional programming problem.

关键词： Semiinfinite programming multiobjective fractional programming generalized invex functions infinitely many equality and inequality constraints parametric duality models duality theorems

A New Approach on Mixed-Type Nondifferentiable Higher-Order Symmetric duality

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Journal of the Operations Research Society of China 2019年第2期7卷 321-335页

作者： Khushboo Verma Pankaj Mathur Tilak Raj Gulati Department of Mathematics and Astronomy University of LucknowLucknow 226001India Department of Mathematics Indian Institute of Technology RoorkeeRoorkee 247667India

In this paper,a new mixed-type higher-order symmetric duality in scalar-objective programming is *** the literature we have results either Wolfe or Mond–Weir-type dual or separately,while in this we have combined those results over one *** weak,strong and converse duality theorems are proved for these programs underη-invexity/η-pseudoinvexity ***-duality is also *** results generalize some existing dual formulations which were discussed by Agarwal et al.(Generalized second-order mixed symmetric duality in nondifferentiable mathematical ***://***/10.1155/2011/103597),Chen(Higher-order symmetric duality in nonlinear nondifferentiable programs),Gulati and Gupta(Wolfe type second order symmetric duality in nondifferentiable ***.310,247–253,2005,Higher order nondifferentiable symmetric duality with generalized ***.329,229–237,2007),Gulati and Verma(Nondifferentiable higher order symmetric duality under invexity/generalized *** 28(8),1661–1674,2014),Hou andYang(On second-order symmetric duality in nondifferentiable programming.J Math Anal Appl.255,488–491,2001),Verma and Gulati(Higher order symmetric duality using generalized ***:Proceeding of 3rd International Conference on Operations Research and Statistics(ORS).***://***/10.5176/2251-1938_ORS13.16,Wolfe type higher order symmetric duality under invexity.J Appl Math Inform.32,153–159,2014).

关键词： Higher-order dual model Symmetric duality duality theorems Higher-order invexity/generalized invexity Self duality

duality FOR A CLASS OF NONS MOOTH MULTIOBJECTIVE PROGRAMMING PROBLEMS

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Journal of Systems Science & Complexity 2005年第1期18卷 74-85页

作者： PENGJianwen YANGXinmin DepartmentofMathematics InnerMongoliaUniversityHohhot010021 ChongqingNormalUniversity Chongqing400047 ChongqingNormalUniversity Chongqing4000471China

In this paper, two new dual models of nonsmooth multiobjective programmingare constructed and two duality results are derived.

关键词： locally lipschitz function multiobjective programming generalizedconvexity duality theorems