Nondifferentiable Multiobjective Programming under Generalized d-ρ-(η,θ)-Type I Univexity

In this paper,on the basis of notions of d-ρ-(η,θ)-invex function,type I function and univex function,we present new classes of generalized d-ρ-(η,θ)-type I univex functions.By using these new concepts,we obtain several sufficient optimality conditions for a feasible solution to be an efficient solution,and derive some Mond-Weir type duality results.     

广义 $d$-$\rho$-$(\eta,\theta)$-type I 一致凸非可微多目标规划

In this puper, on the basis of notions of d-p-（η, θ）-invex function, type I function and univex function, we present new classes of generalized d-p-（η, θ）-type I univex functions. By using these new concepts, we obtain several sufficient optimality conditions for a feasible solution to be an efficient solution, and derive some Mond-Weir type duality results.     

Optimality and duality for multiple-objective optimization under generalized type I univexity

In this paper, we extend the classes of generalized type I vector-valued functions introduced by Aghezzaf and Hachimi in [J. Global Optim. 18 (2000) 91-101] to generalized univex type I vector-valued functions and consider a multiple-objective optimization problem involving generalized type I univex functions. A number of Kuhn-Tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution. The Mond-Weir and general Mond-Weir type duality results are also presented.     

On nonlinear multiple objective fractional programming involving semilocally type-I univex functions

The aim of this paper is to obtain sufficient optimality conditions for a nonlinear multiple objective fractional programming problem involving semilocally type-I univex and related functions. Furthermore, a general dual is formulated and duality results are proved under the assumptions of generalized semilocally type-I univex and related functions. Our results generalize several known results in the literature.     

Sufficiency and duality in nondifferentiable multiobjective programming involving generalized type I functions

Recently, Hachimi and Aghezzaf defined generalized (F,α,ρ,d)-type I functions, a new class of functions that unifies several concepts of generalized type I functions. In this paper, the generalized (F,α,ρ,d)-type I functions are extended to nondifferentiable functions. By utilizing the new concepts, we obtain several sufficient optimality conditions and prove mixed type and Mond-Weir type duality results for the nondifferentiable multiobjective programming problem.     

Nondifferentiable multiobjective programming under generalized d-univexity

In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex, strong pseudoinvex, weak quasi invex, weak pseudoinvex and strong quasi invex functions in Aghezzaf and Hachimi [Numer. Funct. Anal. Optim. 22 (2001) 775], d-invex functions in Antczak [Europ. J. Oper. Res. 137 (2002) 28] and univex functions in Bector et al. [Univex functions and univex nonlinear programming, Proc. Admin. Sci. Assoc. Canada, 1992, p. 115]. By utilizing the new concepts, we derive a Karush–Kuhn–Tucker sufficient optimality condition and establish Mond–Weir type and general Mond–Weir type duality results for the nondifferentiable multiobjective programming problem.     

Some nondifferentiable multiobjective programming under generalized d-V-type-I univexity

In this paper, we introduce new classes of functions called d-V-type-I univex by extending the definition of d-V-type-I functions and consider a multiobjective optimization problem involving generalized d-V-type-I univex functions. A number of Karush–Kuhn–Tucker-type sufficient optimality conditions are obtained for a feasible solution to be a weak Pareto efficient solution. The Mond–Weir-type duality results are also presented. The results obtained in this paper generalize and extend the previously known result in this area.     

Sufficiency and Duality in Multiobjective Variational Problems with Generalized Type I Functions

Recently Hachimi and Aghezzaf introduced the notion of (F,α,ρ,d)-type I functions, a new class of functions that unifies several concepts of generalized type I functions. Here, we extend the concepts of (F,α,ρ,d)-type I and generalized (F,α,ρ, d)-type I functions to the continuous case and we use these concepts to establish various sufficient optimality conditions and mixed duality results for multiobjective variational problems. Our results apparently generalize a fairly large number of sufficient optimality conditions and duality results previously obtained for multiobjective variational problems.     

Optimality conditions and duality in multiple objective programming involving semilocally convex and related functions

A nonlinear multiple objective programming problem is considered where the functions involved are nondifferentiable. By considering the concept of weak minima, the Fritz John type and Karush-Kuhn- Tucker type necessary optimality conditions and Wolfe and Mond-Weir type duality results are given in terms of the right differentials of the functions. The duality results are stated by using the concepts of generalized semilocally convex functions     

Sufficiency and duality in differentiable multiobjective programming involving generalized type I functions

In this paper, new classes of generalized (F,α,ρ,d)-type I functions are introduced for differentiable multiobjective programming. Based upon these generalized functions, first, we obtain several sufficient optimality conditions for feasible solution to be an efficient or weak efficient solution. Second, we prove weak and strong duality theorems for mixed type duality.     

Duality in Vector Optimization Under Type 1 α-Invexity in Banach Spaces

The aim of this paper is to provide global optimality conditions and duality results for a class of nonconvex vector optimization problems posed on Banach spaces. In this paper, we introduce the concept of quasi type I α-invex, pseudo type I α-invex, quasi pseudo type I α-invex, and pseudo quasi type I α-invex functions in the setting of Banach spaces, and we consider a vector optimization problem with functions defined on Banach spaces. A few sufficient optimality conditions are given, and some results on duality are proved.     

Optimality and Duality in Nondifferentiable and Multiobjective Programming under Generalized d-Invexity

In this paper, we are concerned with the nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized d-type-I functions. By utilizing the new concepts, Antczak type Karush-Kuhn-Tucker sufficient optimality conditions, Mond-Weir type and general Mond-Weir type duality results are obtained for non-differentiable and multiobjective programming.     

Complex Minimax Fractional Programming of Analytic Functions

We prove that a minmax fractional programming problem is equivalent to a minimax nonfractional parametric problem for a given parameter in complex space. Using a parametric approach, we establish the Kuhn-Tucker type necessary optimality conditions and prove the existence theorem of optimality for complex minimax fractional programming in the framework of generalized convexity. Subsequently, we apply the optimality conditions to formulate a one-parameter dual problem and prove weak duality, strong duality, and strict converse duality theorems involving generalized convex complex functions. This research was partly supported by NSC, Taiwan.     

Optimality and duality in nonlinear programming involving semilocally B-preinvex and related functions

A nonlinear programming problem is considered where the functions involved are η-semidifferentiable. Fritz John and Karush–Kuhn–Tucker types necessary optimality conditions are obtained. Moreover, a result concerning sufficiency of optimality conditions is given. Wolfe and Mond–Weir types duality results are formulated in terms of η-semidifferentials. The duality results are given using concepts of generalized semilocally B-preinvex functions.     

非光滑多目标广义本性凸规划的最优性条件与对偶

In this paper, we introduce generalized essentially pseudoconvex function and generalized essentially quasiconvex function, and give sufficient optimality conditions of the nonsmooth generalized convex multi-objective programming and its saddle point theorem about cone efficient solution. We set up Mond-Weir type duality and Craven type duality for nonsmooth multiobjective programming with generalized essentially convex functions, and prove them.     

Optimality conditions and duality for a class of nondifferentiable multiobjective generalized fractional programming problems

This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.     

Sufficiency and Duality in Multiobjective Programming under Generalized Type I Functions

In this paper, new classes of generalized (F,α,ρ,d)-V-type I functions are introduced for differentiable multiobjective programming problems. Based upon these generalized convex functions, sufficient optimality conditions are established. Weak, strong and strict converse duality theorems are also derived for Wolfe and Mond-Weir type multiobjective dual programs.     

On nondifferentiable minimax fractional programming under generalized α-type I invexity

In this paper, we study a nondifferentiable minimax fractional programming problem under the assumptions of generalized α-type I invex function. In this paper we introduce the concepts of α-type I invex, pseudo α-type I invex, strict pseudo α-type I invex and quasi α-type I invex functions in the setting of Clarke subdifferential functions. We derive Karush-Kuhn-Tucker type sufficient optimality conditions and establish weak, strong and converse duality theorems for the problem and its three different dual problems. The results in this paper extend several known results in the literature.     

Generalized nonsmooth invexity over cones in vector optimization

In this paper K-nonsmooth quasi-invex and (strictly or strongly) K-nonsmooth pseudo-invex functions are defined. By utilizing these new concepts, the Fritz–John type and Kuhn–Tucker type necessary optimality conditions and number of sufficient optimality conditions are established for a nonsmooth vector optimization problem wherein Clarke’s generalized gradient is used. Further a Mond Weir type dual is associated and weak and strong duality results are obtained.     

On sufficiency and duality for a class of interval-valued programming problems

In this paper, we are concerned with an interval-valued programming problem. Sufficient optimality conditions are established under generalized convex functions for a feasible solution to be an efficient solution. Appropriate duality theorems for Mond-Weir and Wolfe type duals are discussed in order to relate the efficient solutions of primal and dual programs.