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81.
A dual method is presented to solve a linearly constrained optimization problem with convex, polyhedral objective function, along with a fast bounding technique, for the optimum value. The method can be used to solve problems, obtained from LPs, where some of the constraints are not required to be exactly satisfied but are penalized by piecewise linear functions, which are added to the objective function of the original problem. The method generalizes an earlier solution technique developed by Prékopa (1990). Applications to stochastic programming are also presented.This research was supported by the National Science Foundation, Grant No. DMS-9005159.Corresponding author. 相似文献
82.
Jianming Miao 《Mathematical Programming》1995,69(1-3):355-368
An interior-point predictor-corrector algorithm for theP
*()-matrix linear complementarity problem is proposed. The algorithm is an extension of Mizuno—Todd—Ye's predictor—corrector algorithm for linear programming problem. The extended algorithm is quadratically convergent with iteration complexity
. It is the first polynomially and quadratically convergent algorithm for a class of LCPs that are not necessarily monotone. 相似文献
83.
Leonid Khachiyan Khaled Elbassioni Vladimir Gurvich 《Discrete Applied Mathematics》2008,156(11):2020-2034
We consider monotone ∨,∧-formulae φ of m atoms, each of which is a monotone inequality of the form fi(x)?ti over the integers, where for i=1,…,m, fi:Zn?R is a given monotone function and ti is a given threshold. We show that if the ∨-degree of φ is bounded by a constant, then for linear, transversal and polymatroid monotone inequalities all minimal integer vectors satisfying φ can be generated in incremental quasi-polynomial time. In contrast, the enumeration problem for the disjunction of m inequalities is NP-hard when m is part of the input. We also discuss some applications of the above results in disjunctive programming, data mining, matroid and reliability theory. 相似文献
84.
《Journal of Discrete Algorithms》2008,6(4):595-604
The class of fork-free graphs is an extension of claw-free graphs and their subclass of line graphs. The first polynomial-time solution to the maximum weight independent set problem in the class of line graphs, which is equivalent to the maximum matching problem in general graphs, has been proposed by Edmonds in 1965 and then extended to the entire class of claw-free graphs by Minty in 1980. Recently, Alekseev proposed a solution for the larger class of fork-free graphs, but only for the unweighted version of the problem, i.e., finding an independent set of maximum cardinality. In the present paper, we describe the first polynomial-time algorithm to solve the problem for weighted fork-free graphs. 相似文献
85.
86.
Paulo J. S. Silva Jonathan Eckstein 《Computational Optimization and Applications》2006,33(2-3):115-156
We consider the variational inequality problem formed by a general set-valued maximal monotone operator and a possibly unbounded
“box” in
, and study its solution by proximal methods whose distance regularizations are coercive over the box. We prove convergence
for a class of double regularizations generalizing a previously-proposed class of Auslender et al. Using these results, we derive a broadened class of augmented
Lagrangian methods. We point out some connections between these methods and earlier work on “pure penalty” smoothing methods
for complementarity; this connection leads to a new form of augmented Lagrangian based on the “neural” smoothing function.
Finally, we computationally compare this new kind of augmented Lagrangian to three previously-known varieties on the MCPLIB
problem library, and show that the neural approach offers some advantages. In these tests, we also consider primal-dual approaches
that include a primal proximal term. Such a stabilizing term tends to slow down the algorithms, but makes them more robust.
This author was partially supported by CNPq, Grant PQ 304133/2004-3 and PRONEX-Optimization. 相似文献
87.
Martin Anthony 《Discrete Applied Mathematics》2006,154(16):2242-2246
We propose a way of measuring the similarity of a Boolean vector to a given set of Boolean vectors, motivated in part by certain data mining or machine learning problems. We relate the similarity measure to one based on Hamming distance and we develop from this some ways of quantifying the ‘quality’ of a dataset. 相似文献
88.
Gabriela Alexe 《Discrete Applied Mathematics》2006,154(7):1039-1049
In a finite dataset consisting of positive and negative observations represented as real valued n-vectors, a positive (negative) pattern is an interval in Rn with the property that it contains sufficiently many positive (negative) observations, and sufficiently few negative (positive) ones. A pattern is spanned if it does not include properly any other interval containing the same set of observations. Although large collections of spanned patterns can provide highly accurate classification models within the framework of the Logical Analysis of Data, no efficient method for their generation is currently known. We propose in this paper, an incrementally polynomial time algorithm for the generation of all spanned patterns in a dataset, which runs in linear time in the output; the algorithm resembles closely the Blake and Quine consensus method for finding the prime implicants of Boolean functions. The efficiency of the proposed algorithm is tested on various publicly available datasets. In the last part of the paper, we present the results of a series of computational experiments which show the high degree of robustness of spanned patterns. 相似文献
89.
《European Journal of Operational Research》2005,164(1):269-285
This paper addresses the existence of market clearing prices and the economic interpretation of strong duality for integer programs in the economic analysis of markets with nonconvexities (indivisibilities). Electric power markets in which nonconvexities arise from the operating characteristics of generators motivate our analysis; however, the results presented here are general and can be applied to other markets in which nonconvexities are important. We show that the optimal solution to a linear program that solves the mixed integer program has dual variables that: (1) have the traditional economic interpretation as prices; (2) explicitly price integral activities; and (3) clear the market in the presence of nonconvexities. We then show how this methodology can be used to interpret the solutions to nonconvex problems such as the problem discussed by Scarf [Journal of Economic Perspectives 8(4) (1994) 111]. 相似文献
90.
We exhibit links between pseudo-Boolean optimization, graph theory and logic. We show the equivalence of maximizing a pseudo-Boolean
function and finding a maximum weight stable set; symmetrically minimizing a pseudo-Boolean function is shown to be equivalent
to solving a weighted satisfiability problem. 相似文献