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Barbu等人在文[1]中时目标函数和约束算子都是Frechet可微的情况下证明了具有算子约束的数学规划的最优性必要条件.本文将这一问题推广为目标函数为非光滑的情形,给出了具有算子约束的Lipschitz规划的最优性充分条件和必要条件. 相似文献
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《应用数学与计算数学学报》2018,(3)
对二次0-1规划问题进行探讨,在无条件约束的二次0-1规划问题基础上,加入了不等式约束,进而对这类问题的全局最优性条件进行研究.通过解决相应的连续问题和其他一些相关的问题,最后得到了一些全局最优性条件,包括必要条件、充分条件以及充分必要条件. 相似文献
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本文讨论了Ward等人定义的锥方向导数和锥次梯度的性质,建立了一般数学规划的最优性Kuhn-Tucker必要条件. 相似文献
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在本文中,我们提出了双凹规划问题和更一般的广义凹规划问题。我们给出了双凹规划问题的整体最优性条件,并构造了一个有限终止外逼近算法。 相似文献
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在局部凸空间中考虑集值优化问题(VP)在强有效解意义下的Kuhn-Tucker最优性条件.在近似锥.次类凸假设下利用择一性定理得到了(VP)取得强有效解的必要条件,利用基泛函的性质给出了(VP)取得强有效解的充分条件,最后给出了一种与(VP)等价的无约束规划。 相似文献
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价格控制问题的基本性质 总被引:5,自引:0,他引:5
价格控制问题是一类重要的二层规划问题。最近,文[3,4]讨论了价格控制问题的最优性条件和解集的性质。本文先用反例说明[3]中关于价格控制问题的可行解的充分必要条件的一个命题是不确切的,并对[4]中基于该命题证得的不可靠结论在适当条件下进行了证明。 相似文献
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在弧连通锥-凸假设下讨论Hausdorff局部凸空间中的一类数学规划的最优性条件问题.首先,利用择一定理得到了锥约束标量优化问题的一个必要最优性条件.其次,利用凸集分离定理证明了无约束向量优化问题关于弱极小元的标量化定理和一个一致的充分必要条件.所得结果深化和丰富了最优化理论及其应用的内容. 相似文献
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We prove the following theorem which gives a bound on the proximity of the real and the integer solutions to certain constrained optimization programs. 相似文献
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G. Kindervater A. Volgenant G. de Leve V. van Gijlswijk 《European Journal of Operational Research》1985,19(1):76-81
For the linear assignment problem we describe how to obtain different dual solutions. It turns out that a shortest path algorithm can be used to compute such solutions with several interesting properties that enable to do better post-optimality analysis.Two examples illustrate how different dual solutions can be used in the context of the traveling salesman problem. 相似文献
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Wilhelm Hummeltenberg 《European Journal of Operational Research》1984,17(1):1-15
Special ordered sets (SOS) have been introduced as a practical device for efficiently handling special classes of nonconvex optimization problems. They are now implemented in most commercial codes for mathematical programming (MP software). The paper gives a survey of possible applications as multiple choice restrictions, conditional multiple choice restrictions, discrete variables, discontinuous variables and piecewise linear functions, global optimization of separable programming problems, alternative right-hand sides, overlapping special ordered sets and the solution of quadratic programming problems. Alternative problem formulations are discussed. Since special ordered sets are not defined uniquely modelling facilities depend on the definition of a special orderedset in a code. The paper demonstrates the superiority of SOS to the application of binary variables if they are treated judiciously. 相似文献
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We present an algorithm for generating a subset of non-dominated vectors of multiple objective mixed integer linear programming. Starting from an initial non-dominated vector, the procedure finds at each iteration a new one that maximizes the infinity-norm distance from the set dominated by the previously found solutions. When all variables are integer, it can generate the whole set of non-dominated vectors. 相似文献
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This paper addresses classes of assembled printed circuit boards, which faces certain kinds of errors during its process of
manufacturing. Occurrence of errors may lead the manufacturer to be in loss. The encountered problem has two objective functions,
one is fractional and the other is a non-linear objective. The manufacturers are confined to maximize the fractional objective
and to minimize the non-linear objective subject to stochastic and non-stochastic environment. This problem is decomposed
into two problems. A solution approach to this model has been developed in this paper. Results of some test problems are provided. 相似文献
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《Optimization》2012,61(6):809-823
By perturbing properly a linear program to a separable quadratic program it is possible to solve the latter in its dual variable space by iterative techniques such as sparsity-preserving SOR (successive overtaxation techniques). In this way large sparse linear programs can be handled. In this paper we give a new computational criterion to check whether the solution of the perturbed quadratic program provides the least 2-norm solution of the original linear program. This criterion improves on the criterion proposed in an earlier paper. We also describe an algorithm for solving linear programs which is based on the SOR methods. The main property of this algorithm is that, under mild assumptions, it finds the least 2-norm solution of a linear program in a finite number of iteration.s 相似文献
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A family of complementarity problems is defined as extensions of the well-known linear complementarity problem (LCP). These are:
A number of well-known mathematical programming problems [namely, quadratic programming (convex, nonconvex, pseudoconvex, nonconvex), linear variational inequalities, bilinear programming, game theory, zero-one integer programming, fixed-charge problem, absolute value programming, variable separable programming] are reformulated as members of this family of four complementarity problems. A brief discussion of the main algorithms for these four problems is presented, together with some computational experience. 相似文献
(i) | second linear complementarity problem (SLCP), which is an LCP extended by introducing further equality restrictions and unrestricted variables; |
(ii) | minimum linear complementarity problem (MLCP), which is an LCP with additional variables not required to be complementary and with a linear objective function which is to be minimized; |
(iii) | second minimum linear complementarity problem (SMLCP), which is an MLCP, but the nonnegative restriction on one of each pair of complementary variables is relaxed so that it is allowed to be unrestricted in value. |
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本文介绍了运筹学在大庆油田开发过程中的一些应用情况,初步展望了运筹学方法在大庆油田开发中进一步应用的前景. 相似文献
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T. Terlaky 《European Journal of Operational Research》1985,22(1):70-100
Our paper treats the primal and dual program of ?p programming. ?p programming is a generalization of ?p approximation problems. There is a strict connection between ?p programming and geometrical programming, because in both of them geometrical inequality plays a fundamental role. The structure of our paper follows that of Klafszkys [1].In the first Sections duality theorems are proved, which play an important role in mathematical programming. Most of these results can be found in Petersons and Eckers [3,4,5], but our proofs are much more simple and we show these fundamental properties more detailed.Afterwards the relation between the Lagrange function and the optimal solution pair is investigated. Regularity is investigated as well and we show the marginal value of ?p programming. In the end linear programming ?p constrained ?p approximation problems, the quadratically constrained quadratic programming and compromise programming are shown as special cases of ?p programming. 相似文献
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We develop algorithms to construct inner approximations of the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linear algebraic approximation suggested recently by Ahmadi and Majumdar, we describe an iterative process through which our approximation is improved at every step. This is done using ideas from column generation in large-scale linear programming. We then apply these techniques to approximate the sum of squares cone in a nonconvex polynomial optimization setting, and the copositive cone for a discrete optimization problem. 相似文献