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71.
Dalila B. M. M. Fontes Eleni Hadjiconstantinou Nicos Christofides 《Journal of Global Optimization》2006,34(1):97-125
In this paper we obtain Lower Bounds (LBs) to concave cost network flow problems. The LBs are derived from state space relaxations
of a dynamic programming formulation, which involve the use of non-injective mapping functions guaranteing a reduction on
the cardinality of the state space. The general state space relaxation procedure is extended to address problems involving
transitions that go across several stages, as is the case of network flow problems. Applications for these LBs include: estimation
of the quality of heuristic solutions; local search methods that use information of the LB solution structure to find initial
solutions to restart the search (Fontes et al., 2003, Networks, 41, 221–228); and branch-and-bound (BB) methods having as
a bounding procedure a modified version of the LB algorithm developed here, (see Fontes et al., 2005a). These LBs are iteratively
improved by penalizing, in a Lagrangian fashion, customers not exactly satisfied or by performing state space modifications.
Both the penalties and the state space are updated by using the subgradient method. Additional constraints are developed to
improve further the LBs by reducing the searchable space. The computational results provided show that very good bounds can
be obtained for concave cost network flow problems, particularly for fixed-charge problems. 相似文献
72.
Searching for a counterfeit coin with two unreliable weighings 总被引:1,自引:0,他引:1
We provide a worst-case optimal procedure to identify one unknown heavy coin among N identically looking coins when a balance scale is used and at most two weighing results can be erroneous. The exact minimal number of weighings is determined. This solves completely the weighing problem of the case of two unreliable weighings. 相似文献
73.
Hansjörg Albrecher 《Operations Research Letters》2005,33(2):183-186
We generalize and sharpen results of Burkard and Fincke concerning the asymptotic behaviour of a certain class of combinatorial optimization problems with bottleneck objective function. In this way several open questions are answered. 相似文献
74.
John Ellis 《Discrete Applied Mathematics》2008,156(5):545-555
We present proofs of lower bounds on the node search number of some grid-like graphs including two-dimensional grids, cylinders, tori and a variation we call “orb-webs”. Node search number is equivalent to pathwidth and vertex separation, which are all important graph parameters. Since matching upper bounds are not difficult to obtain, this implies that the pathwidth of these graphs is easily computed, because the bounds are simple functions of the graph dimensions. We also show matching upper and lower bounds on the node search number of equidimensional tori which are one less than the obvious upper bound. 相似文献
75.
L.Yu. Kolotilina 《Linear algebra and its applications》2008,429(10):2521-2539
The paper considers the sharpness problem for certain two-sided bounds for the Perron root of an irreducible nonnegative matrix. The results obtained are applied to prove the sharpness of the related eigenvalue inclusion sets in classes of matrices with fixed diagonal entries, bounded above deleted absolute row sums, and a partly specified irreducible sparsity pattern. 相似文献
76.
In this paper we consider a collocation method for solving Fredholm integral equations of the first kind, which is known to be an ill-posed problem. An “unregularized” use of this method can give reliable results in the case when the rate at which smallest singular values of the collocation matrices decrease is known a priori. In this case the number of collocation points plays the role of a regularization parameter. If the a priori information mentioned above is not available, then a combination of collocation with Tikhonov regularization can be the method of choice. We analyze such regularized collocation in a rather general setting, when a solution smoothness is given as a source condition with an operator monotone index function. This setting covers all types of smoothness studied so far in the theory of Tikhonov regularization. One more issue discussed in this paper is an a posteriori choice of the regularization parameter, which allows us to reach an optimal order of accuracy for deterministic noise model without any knowledge of solution smoothness. 相似文献
77.
We consider a spatial interaction model for locating a set of new facilities that compete for customer demand with each other, as well as with some pre-existing facilities to capture the “market expansion” and the “market cannibalization” effects. Customer demand is assumed to be a concave non-decreasing function of the total utility derived by each customer from the service offered by the facilities. The problem is formulated as a non-linear Knapsack problem, for which we develop a novel solution approach based on constructing an efficient piecewise linear approximation scheme for the objective function. This allows us to develop exact and α-optimal solution approaches capable of dealing with relatively large-scale instances of the model. We also develop a fast Heuristic Algorithm for which a tight worst-case error bound is established. 相似文献
78.
E. R. Jakobsen 《BIT Numerical Mathematics》2004,44(2):269-285
In this paper we provide estimates of the rates of convergence of monotone approximation schemes for non-convex equations in one space-dimension. The equations under consideration are the degenerate elliptic Isaacs equations with x-depending coefficients, and the results applies in particular to certain finite difference methods and control schemes based on the dynamic programming principle. Recently, Krylov, Barles, and Jakobsen obtained similar estimates for convex Hamilton–Jacobi–Bellman equations in arbitrary space-dimensions. Our results are only valid in one space-dimension, but they are the first results of this type for non-convex second-order equations. 相似文献
79.
Dimitris Bertsimas 《Queueing Systems》1995,21(3-4):337-389
We survey a new approach that the author and his co-workers have developed to formulate stochastic control problems (predominantly queueing systems) asmathematical programming problems. The central idea is to characterize the region of achievable performance in a stochastic control problem, i.e., find linear or nonlinear constraints on the performance vectors that all policies satisfy. We present linear and nonlinear relaxations of the performance space for the following problems: Indexable systems (multiclass single station queues and multiarmed bandit problems), restless bandit problems, polling systems, multiclass queueing and loss networks. These relaxations lead to bounds on the performance of an optimal policy. Using information from the relaxations we construct heuristic nearly optimal policies. The theme in the paper is the thesis that better formulations lead to deeper understanding and better solution methods. Overall the proposed approach for stochastic control problems parallels efforts of the mathematical programming community in the last twenty years to develop sharper formulations (polyhedral combinatorics and more recently nonlinear relaxations) and leads to new insights ranging from a complete characterization and new algorithms for indexable systems to tight lower bounds and nearly optimal algorithms for restless bandit problems, polling systems, multiclass queueing and loss networks. 相似文献
80.
Empirical minimization 总被引:3,自引:0,他引:3
We investigate the behavior of the empirical minimization algorithm using various methods. We first analyze it by comparing
the empirical, random, structure and the original one on the class, either in an additive sense, via the uniform law of large
numbers, or in a multiplicative sense, using isomorphic coordinate projections. We then show that a direct analysis of the
empirical minimization algorithm yields a significantly better bound, and that the estimates we obtain are essentially sharp.
The method of proof we use is based on Talagrand's concentration inequality for empirical processes.
Research partially supported by NSF under award DMS-0434393.
Research partially supported by the Australian Research Council Discovery Porject DP0343616. 相似文献