共查询到20条相似文献,搜索用时 725 毫秒
1.
Optimality and duality with generalized convexity 总被引:4,自引:0,他引:4
N. G. Rueda M. A. Hanson C. Singh 《Journal of Optimization Theory and Applications》1995,86(2):491-500
Hanson and Mond have given sets of necessary and sufficient conditions for optimality and duality in constrained optimization by introducing classes of generalized convex functions, called type I and type II functions. Recently, Bector defined univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, optimality and duality results for several mathematical programs are obtained combining the concepts of type I and univex functions. Examples of functions satisfying these conditions are given. 相似文献
2.
Multiple objective fractional programming involving semilocally type I-preinvex and related functions 总被引:1,自引:0,他引:1
S.K. Mishra S.Y. Wang K.K. Lai 《Journal of Mathematical Analysis and Applications》2005,310(2):626-640
Sufficient optimality conditions are obtained for a nonlinear multiple objective fractional programming problem involving η-semidifferentiable type I-preinvex and related functions. Furthermore, a general dual is formulated and duality results are proved under the assumptions of generalized semilocally type I-preinvex and related functions. Our result generalize the results of Preda [V. Preda, Optimality and duality in fractional multiple objective programming involving semilocally preinvex and related functions, J. Math. Anal. Appl. 288 (2003) 365–382] and Stancu-Minasian [I.M. Stancu-Minasian, Optimality and duality in fractional programming involving semilocally preinvex and related functions, J. Inform. Optim. Sci. 23 (2002) 185–201]. 相似文献
3.
Pseudoconvexity of a function on one set with respect to some other set is defined and duality theorems are proved for nonlinear programming problems by assuming a certain kind of convexity property for a particular linear combination of functions involved in the problem rather than assuming the convexity property for the individual functions as is usually done. This approach generalizes some of the well-known duality theorems and gives some additional strict converse duality theorems which are not comparable with the earlier duality results of this type. Further it is shown that the duality theory for nonlinear fractional programming problems follows as a particular case of the results established here. 相似文献
4.
We introduce higher‐order duality (Mangasarian type and Mond–Wier type) of variational problems. Under higher‐order generalized invexity assumptions on functions that compose the primal problem, higher‐order duality results (weak duality, strong duality, and converse duality) are derived for this pair of problems. Also, we establish many examples and counter‐examples to support our investigation. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
5.
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. 相似文献
6.
本文研究带不等式和等式约束的多目标规划的Mond-Weir型对偶性理论。在目标和约束是广义凸的假设下,证明了弱对偶定理、直接对偶定理以及逆对偶定理 相似文献
7.
Optimality and Duality in Nondifferentiable and Multiobjective Programming under Generalized d-Invexity 总被引:1,自引:1,他引:0
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. 相似文献
8.
Two pairs of non-differentiable multiobjective symmetric dual problems with cone constraints over arbitrary cones, which are Wolfe type and Mond–Weir type, are considered. On the basis of weak efficiency with respect to a convex cone, we obtain symmetric duality results for the two pairs of problems under cone-invexity and cone-pseudoinvexity assumptions on the involved functions. Our results extend the results in Khurana [S. Khurana, Symmetric duality in multiobjective programming involving generalized cone-invex functions, European Journal of Operational Research 165 (2005) 592–597] to the non-differentiable multiobjective symmetric dual problem. 相似文献
9.
Optimality and duality for multiple-objective optimization under generalized type I univexity 总被引:1,自引:0,他引:1
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. 相似文献
10.
11.
《European Journal of Operational Research》2005,165(3):592-597
In this paper, cone-pseudoinvex and strongly cone-pseudoinvex functions are defined. A pair of Mond–Weir type symmetric dual multiobjective programs is formulated over arbitrary cones. Weak duality, strong duality and converse duality theorems are established using the above-defined functions. A self-duality theorem is also given by assuming the functions involved to be skew-symmetric. 相似文献
12.
Li-ping Pang Wei Wang Zun-quan Xia 《应用数学学报(英文版)》2006,22(1):49-58
The form of a dual problem of Mond-Weir type for multi-objective programming problems of generalized functions is defined and theorems of the weak duality, direct duality and inverse duality are proven. 相似文献
13.
《European Journal of Operational Research》1998,107(3):675-685
Necessary optimality conditions are established for a multiobjective nonlinear programming problem involving semilocally convex and related functions in terms of their right differentials. Wolfe type and Mond-Weir type duals are formulated and duality results are proved under the assumptions of semilocal convexity, semilocal quasiconvexity and semilocal pseudoconvexity. 相似文献
14.
A mixed type dual to a programming problem containing support functions in a objective as well as constraint functions is formulated and various duality results are validated under generalized convexity and invexity conditions. Several known results are deducted as special cases. 相似文献
15.
群体多目标规划的联合Mond-Weir对偶 总被引:5,自引:0,他引:5
对于目标和约束均为不对称的群体多目标规划问题,本文研究它的联合有效解类 的Mond—Weir型对偶性,得到了相应的弱对偶定理、直接对偶定理和逆对偶定理. 相似文献
16.
Some properties of arcwise connected functions in terms of their directional derivatives are investigated. These properties are then utilized to establish necessary and sufficient optimality conditions for scalar-valued nonlinear programming problems. Mond–Weir type duality results are also proved. 相似文献
17.
In this paper we generalize the concept of a Dini-convex function with Dini derivative and introduce a new concept - Dini-invexity. Some properties of Dini invex functions are discussed. On the base of this, we study the Wolfe type duality and Mond-Weir type duality for Dini-invex nonsmooth multiobjective programmings and obtain corresponding duality theorems. 相似文献
18.
In 1951, Fenchel discovered a special duality, which relates the minimization of a sum of two convex functions with the maximization
of the sum of concave functions, using conjugates. Fenchel's duality is central to the study of constrained optimization.
It requires an existence of an interior point of a convex set which often has empty interior in optimization applications.
The well known relaxations of this requirement in the literature are again weaker forms of the interior point condition. Avoiding
an interior point condition in duality has so far been a difficult problem. However, a non-interior point type condition is
essential for the application of Fenchel's duality to optimization. In this paper we solve this problem by presenting a simple
geometric condition in terms of the sum of the epigraphs of conjugate functions. We also establish a necessary and sufficient
condition for the ε-subdifferential sum formula in terms of the sum of the epigraphs of conjugate functions. Our results offer further insight
into Fenchel's duality.
Dedicated to Terry Rockafellar on his 70th birthday 相似文献
19.
本文研究了一类多目标控制问题的混合对偶性.利用函数的广义V-不变凸性条件,得出了关于有效解的弱对偶定理、强对偶定理和严格逆对偶定理,推广了多目标控制问题的对偶性结论. 相似文献