共查询到10条相似文献,搜索用时 93 毫秒
1.
Gregory D. Glockner George L. Nemhauser Craig A. Tovey 《Computational Optimization and Applications》2001,18(3):233-250
In a multiperiod dynamic network flow problem, we model uncertain arc capacities using scenario aggregation. This model is so large that it may be difficult to obtain optimal integer or even continuous solutions. We develop a Lagrangian decomposition method based on the structure recently introduced in G.D. Glockner and G.L. Nemhauser, Operations Research, vol. 48, pp. 233–242, 2000. Our algorithm produces a near-optimal primal integral solution and an optimum solution to the Lagrangian dual. The dual is initialized using marginal values from a primal heuristic. Then, primal and dual solutions are improved in alternation. The algorithm greatly reduces computation time and memory use for real-world instances derived from an air traffic control model. 相似文献
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Chandal Nahak 《Rendiconti del Circolo Matematico di Palermo》1998,47(2):191-206
Wolfe and Mond-Weir type duals for multiobjective control problems are formulated. Under pseudo-invexity/quasi-invexity assumptions
on the functions involved, weak and strong duality theorems are proved to relate efficient solutions of the primal and dual
problems. 相似文献
5.
N. Mahdavi-Amiri F. Salehi Sadaghiani 《4OR: A Quarterly Journal of Operations Research》2017,15(3):303-326
Recently, Luc defined a dual program for a multiple objective linear program. The dual problem is also a multiple objective linear problem and the weak duality and strong duality theorems for these primal and dual problems have been established. Here, we use these results to prove some relationships between multiple objective linear primal and dual problems. We extend the available results on single objective linear primal and dual problems to multiple objective linear primal and dual problems. Complementary slackness conditions for efficient solutions, and conditions for the existence of weakly efficient solution sets and existence of strictly primal and dual feasible points are established. We show that primal-dual (weakly) efficient solutions satisfying strictly complementary conditions exist. Furthermore, we consider Isermann’s and Kolumban’s dual problems and establish conditions for the existence of strictly primal and dual feasible points. We show the existence of primal-dual feasible points satisfying strictly complementary conditions for Isermann’s dual problem. Also, we give an alternative proof to establish necessary conditions for weakly efficient solutions of multiple objective programs, assuming the Kuhn–Tucker (KT) constraint qualification. We also provide a new condition to ensure the KT constraint qualification. 相似文献
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Magnus Önnheim Emil Gustavsson Ann-Brith Strömberg Michael Patriksson Torbjörn Larsson 《Mathematical Programming》2017,163(1-2):57-84
Consider the utilization of a Lagrangian dual method which is convergent for consistent convex optimization problems. When it is used to solve an infeasible optimization problem, its inconsistency will then manifest itself through the divergence of the sequence of dual iterates. Will then the sequence of primal subproblem solutions still yield relevant information regarding the primal program? We answer this question in the affirmative for a convex program and an associated subgradient algorithm for its Lagrange dual. We show that the primal–dual pair of programs corresponding to an associated homogeneous dual function is in turn associated with a saddle-point problem, in which—in the inconsistent case—the primal part amounts to finding a solution in the primal space such that the Euclidean norm of the infeasibility in the relaxed constraints is minimized; the dual part amounts to identifying a feasible steepest ascent direction for the Lagrangian dual function. We present convergence results for a conditional \(\varepsilon \)-subgradient optimization algorithm applied to the Lagrangian dual problem, and the construction of an ergodic sequence of primal subproblem solutions; this composite algorithm yields convergence of the primal–dual sequence to the set of saddle-points of the associated homogeneous Lagrangian function; for linear programs, convergence to the subset in which the primal objective is at minimum is also achieved. 相似文献
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Solutions and optimality criteria for nonconvex quadratic-exponential minimization problem 总被引:1,自引:0,他引:1
This paper presents a set of complete solutions and optimality conditions for a nonconvex quadratic-exponential optimization
problem. By using the canonical duality theory developed by the first author, the nonconvex primal problem in n-dimensional space can be converted into an one-dimensional
canonical dual problem with zero duality gap, which can be solved easily to obtain all dual solutions. Each dual solution
leads to a primal solution. Both global and local extremality conditions of these primal solutions can be identified by the
triality theory associated with the canonical duality theory. Several examples are illustrated. 相似文献
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P. H. Sach D. S. Kim L. A. Tuan G. M. Lee 《Journal of Optimization Theory and Applications》2008,136(1):105-123
In this paper, we introduce new dual problems of generalized vector variational inequality problems with set-valued maps and
we discuss a link between the solution sets of the primal and dual problems. The notion of solutions in each of these problems
is introduced via the concepts of efficiency, weak efficiency or Benson proper efficiency in vector optimization. We provide
also examples showing that some earlier duality results for vector variational inequality may not be true.
This work was supported by the Brain Korea 21 Project in 2006. 相似文献
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In exact arithmetic, the simplex method applied to a particular linear programming problem instance with real data either shows that it is infeasible, shows that its dual is infeasible, or generates optimal solutions to both problems. Most interior-point methods, on the other hand, do not provide such clear-cut information. If the primal and dual problems have bounded nonempty sets of optimal solutions, they usually generate a sequence of primal or primaldual iterates that approach feasibility and optimality. But if the primal or dual instance is infeasible, most methods give less precise diagnostics. There are methods with finite convergence to an exact solution even with real data. Unfortunately, bounds on the required number of iterations for such methods applied to instances with real data are very hard to calculate and often quite large. Our concern is with obtaining information from inexact solutions after a moderate number of iterations. We provide general tools (extensions of the Farkas lemma) for concluding that a problem or its dual is likely (in a certain well-defined sense) to be infeasible, and apply them to develop stopping rules for a homogeneous self-dual algorithm and for a generic infeasible-interior-point method for linear programming. These rules allow precise conclusions to be drawn about the linear programming problem and its dual: either near-optimal solutions are produced, or we obtain certificates that all optimal solutions, or all feasible solutions to the primal or dual, must have large norm. Our rules thus allow more definitive interpretation of the output of such an algorithm than previous termination criteria. We give bounds on the number of iterations required before these rules apply. Our tools may also be useful for other iterative methods for linear programming. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V. 相似文献
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日本是世界上保险业最发达的国家之一.但自20世纪90年代以来随着泡沫经济的破灭,宏观经济和金融环境的恶化,日本保险业尤其是寿险业进入了停滞与调整期.面对这一情况,日本政府层面和公司层面都推出各种措施,振兴踯躅前行中的日本寿险业.利用数据包络分析(DEA)方法对1998 2008年期间日本全部寿险公司的技术效率、纯技术效率和规模效率及其变动趋势进行了测度,对日本寿险市场的发展演变历程进行全面分析,希望对中国寿险业的发展提供经验借鉴. 相似文献