共查询到20条相似文献,搜索用时 15 毫秒
1.
Hsien-Chung Wu 《Fuzzy Optimization and Decision Making》2003,2(1):61-73
The concept of fuzzy scalar (inner) product that will be used in the fuzzy objective and inequality constraints of the fuzzy primal and dual linear programming problems with fuzzy coefficients is proposed in this paper. We also introduce a solution concept that is essentially similar to the notion of Pareto optimal solution in the multiobjective programming problems by imposing a partial ordering on the set of all fuzzy numbers. We then prove the weak and strong duality theorems for fuzzy linear programming problems with fuzzy coefficients. 相似文献
2.
A duality theory for algebraic linear (integer) programming (ALP) is developed which is of the same importance for linear (integer) programming with linear algebraic objectives as linear programming duality is for classical LP. In particular, optimality criteria for primal, primal-dual, and dual methods are given which generalize feasibility and complementarity criteria of classical LP. Strong duality results are given for special combinatorial problems. Further, the validity and finiteness of a primal simplex method based on a feasibility criterion are proved in the case of nondiscrete variables. In this case a strong duality result is shown. 相似文献
3.
We continue the study of approximation properties of alternative duality schemes for improper problems of linear programming. The schemes are based on the use of the classical Lagrange function regularized simultaneously in primal and dual variables. The earlier results on the connection of its saddle points with the lexicographic correction of the right-hand sides of constraints in improper problems of the first and second kind are transferred to a more general type of improperness. Convergence theorems are presented and an informal interpretation of the obtained generalized solution is given. 相似文献
4.
Ching-Feng Wen 《Numerical Functional Analysis & Optimization》2013,34(1):80-129
This article proposes a practical computational procedure to solve a class of continuous-time linear fractional programming problems by designing a discretized problem. Using the optimal solutions of proposed discretized problems, we construct a sequence of feasible solutions of continuous-time linear fractional programming problem and show that there exists a subsequence that converges weakly to a desired optimal solution. We also establish an estimate of the error bound. Finally, we provide two numerical examples to demonstrate the usefulness of this practical algorithm. 相似文献
5.
On Linear Programming Duality and Necessary and Sufficient Conditions in Minimax Theory 总被引:1,自引:0,他引:1
J. B. G. Frenk P. Kas G. Kassay 《Journal of Optimization Theory and Applications》2007,132(3):423-439
In this paper we discuss necessary and sufficient conditions for different minimax results to hold using only linear programming
duality and the finite intersection property for compact sets. It turns out that these necessary and sufficient conditions
have a clear interpretation within zero-sum game theory. We apply these results to derive necessary and sufficient conditions
for strong duality for a general class of optimization problems.
The authors like to thank the comments of the anonymous referees for their remarks, which greatly improved the presentation
of this paper. 相似文献
6.
Wolfe Duality for Interval-Valued Optimization 总被引:1,自引:0,他引:1
H. C. Wu 《Journal of Optimization Theory and Applications》2008,138(3):497-509
Weak and strong duality theorems in interval-valued optimization problem based on the formulation of the Wolfe primal and
dual problems are derived. The solution concepts of the primal and dual problems are based on the concept of nondominated
solution employed in vector optimization problems. The concepts of no duality gap in the weak and strong sense are also introduced,
and strong duality theorems in the weak and strong sense are then derived. 相似文献
7.
针对下层为线性规划的非线性双层规划问题,提出了一种基于下层对偶理论的遗传算法。首先利用下层对偶问题可行域的极点对上层变量的取值域进行划分,使得每一个划分区域对应一个极点。根据原一对偶问题最优解的关系,确定每个划分区域对应的下层最优解。其次利用罚函数方法处理了上层约束,设计了一个依赖于种群变化的动态罚因子。对20个测试问题的数值结果表明,所提出的算法是可行有效的。 相似文献
8.
In this paper, we are concerned with the multiobjective programming problem with inequality constraints. We introduce new classes of generalized type I vector-valued functions. Duality theorems are proved for Mond–Weir and general Mond–Weir type duality under the above generalized type I assumptions. 相似文献
9.
Hsien-Chung Wu 《Fuzzy Optimization and Decision Making》2004,3(4):345-365
A solution concept of fuzzy optimization problems, which is essentially similar to the notion of Pareto optimal solution (nondominated solution) in multiobjective programming problems, is introduced by imposing a partial ordering on the set of all fuzzy numbers. We also introduce a concept of fuzzy scalar (inner) product based on the positive and negative parts of fuzzy numbers. Then the fuzzy-valued Lagrangian function and the fuzzy-valued Lagrangian dual function for the fuzzy optimization problem are proposed via the concept of fuzzy scalar product. Under these settings, the weak and strong duality theorems for fuzzy optimization problems can be elicited. We show that there is no duality gap between the primal and dual fuzzy optimization problems under suitable assumptions for fuzzy-valued functions. 相似文献
10.
This paper is concerned with second-order duality for a class of nondifferentiable multiobjective programming problems. Usual duality theorems are proved for Mangasarian type and general Mond–Weir type vector duals under generalized bonvexity assumptions. 相似文献
11.
本文讨论F—广义凸多目标规划的对偶理论,证明了弱对偶、直接对偶和逆对偶定理.主要结果参考文献[1]的推广和发展。 相似文献
12.
A class of fuzzy linear programming (FLP) problems based on fuzzy relations is introduced, the concepts of feasible and -efficient solutions are defined. The class of crisp (classical) LP problems and interval LP problems can be embedded into the class of FLP ones. Moreover, for FLP problems a new concept of duality is introduced and the weak and strong duality theorems are derived. The previous results are applied to the special case of interval LP and compared to the existing literature. 相似文献
13.
14.
A two person zero-sum matrix game with fuzzy goals is shown to be equivalent to a primal-dual pair of fuzzy linear programming problems. Further certain difficulties with similar studies reported in the literature are also discussed. 相似文献
15.
For a multiobjective bilevel programming problem(P) with an extremal-value function,its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved.Under some convexity and monotonicity assumptions,the weak and strong duality assertions are obtained. 相似文献
16.
Edward L. Hannan 《The Journal of the Operational Research Society》1978,29(7):643-649
The dual of the multiple objective linear programming problem is defined as a multiparametric LP problem for the right-hand sides. The resulting dual variables are multidimensional and are related to the indifference regions in the primal problem. The formulation of the dual is shown to be preferable to the vector minimization formulation in terms of (a) identifying primal efficient points and indifference regions, and (b) sensitivity analysis. 相似文献
17.
18.
C. C. Gonzaga 《Journal of Optimization Theory and Applications》2007,135(3):333-342
We present a method for constructing linear programming problems with randomly generated data. Besides the number of variables
and constraints, the dimensions of the primal and dual faces are given. We show that, for problems in which the constraint
matrix is carelessly constructed with random entries, with probability one only one between primal degeneracy and dual degeneracy
appears. 相似文献
19.
20.
Patrizia Daniele Sofia Giuffrè Antonino Maugeri Fabio Raciti 《Journal of Optimization Theory and Applications》2014,162(3):718-734
This paper is concerned with the problem of strong duality between an infinite dimensional convex optimization problem with cone and equality constraints and its Lagrange dual. A necessary and sufficient condition and sufficient conditions, really new, in order that the strong duality holds true are given. As an application, the existence of the Lagrange multiplier associated with the obstacle problem and to an elastic–plastic torsion problem, more general than the ones previously considered, is stated together with a characterization of the elastic–plastic torsion problem. This application is the main result of the paper. It is worth remarking that the usual conditions based on the interior, on the core, on the intrinsic core or on the strong quasi-relative interior cannot be used because they require the nonemptiness of the interior (and of the above mentioned generalized interior concepts) of the ordering cone, which is usually empty. 相似文献