A new method for computing exact experimental designs for linear regression models by integer quadratic programming is proposed. The key idea is to use the criterion of DQ-optimality, which is a quadratic approximatio...
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A new method for computing exact experimental designs for linear regression models by integer quadratic programming is proposed. The key idea is to use the criterion of DQ-optimality, which is a quadratic approximation of the criterion of D-optimality in the neighbourhood of the approximate D-optimal information matrix. Several numerical examples are used to demonstrate that the D-efficiency of exact DQ-optimal designs is usually very high. An important advantage of this method is that it can be applied to situations with general linear constraints on permissible designs, including marginal and cost constraints. (C) 2013 Elsevier B.V. All rights reserved.
In this paper. a new variable reduction technique is presented for general integer quadratic programming problem (GP), under which some variables of (GP) can be fixed at zero without sacrificing optimality. A sufficie...
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In this paper. a new variable reduction technique is presented for general integer quadratic programming problem (GP), under which some variables of (GP) can be fixed at zero without sacrificing optimality. A sufficient condition and a necessary condition for the identification of dominated terms are provided. By comparing the given data of the problem and the upper bound of the variables, if they meet certain conditions, some variables can be fixed at zero. We report a computational study to demonstrate the efficacy of the proposed technique in solving general integer quadratic programming problems. Furthermore, we discuss separable integer quadratic programming problems in a simpler and clearer form. (c) 2009 Elsevier Inc. All rights reserved.
Mixed integer quadratic programming (MIQP) is the problem of minimizing a quadratic function over mixed integer points in a rational polyhedron. This paper focuses on the augmented Lagrangian dual (ALD) for MIQP. ALD ...
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Mixed integer quadratic programming (MIQP) is the problem of minimizing a quadratic function over mixed integer points in a rational polyhedron. This paper focuses on the augmented Lagrangian dual (ALD) for MIQP. ALD augments the usual Lagrangian dual with a weighted nonlinear penalty on the dualized constraints. We first prove that ALD will reach a zero duality gap asymptotically as the weight on the penalty goes to infinity under some mild conditions on the penalty function. We next show that a finite penalty weight is enough for a zero gap when we use any norm as the penalty function. Finally, we prove a polynomial bound on the weight on the penalty term to obtain a zero gap.
We consider the NP-hard problem of minimizing a separable concave quadratic function over the integral points in a polyhedron, and we denote by Delta the largest absolute value of the subdeterminants of the constraint...
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We consider the NP-hard problem of minimizing a separable concave quadratic function over the integral points in a polyhedron, and we denote by Delta the largest absolute value of the subdeterminants of the constraint matrix. In this paper we give an algorithm that finds an epsilon-approximate solution for this problem by solving a number of integer linear programs whose constraint matrices have subdeterminants bounded by Delta in absolute value. The number of these integer linear programs is polynomial in the dimension n, in Delta, and in 1/epsilon, provided that the number k of variables that appear nonlinearly in the objective is fixed. As a corollary, we obtain the first polynomial-time approximation algorithm for separable concave integer quadratic programming with Delta <= 2 and k fixed. In the totally unimodular case Delta = 1, we give an improved algorithm that only needs to solve a number of linear programs that is polynomial in 1/epsilon and is independent of n, provided that k is fixed.
A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of n Delta on the proximity of optimal solutions of an integer Linear programming problem and its standard linear relaxation. In this bo...
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A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of n Delta on the proximity of optimal solutions of an integer Linear programming problem and its standard linear relaxation. In this bound, n is the number of variables and Delta denotes the maximum of the absolute values of the subdeterminants of the constraint matrix. Hochbaum and Shanthikumar, and Werman and Magagnosc showed that the same upper bound is valid if a more general convex function is minimized, instead of a linear function. No proximity result of this type is known when the objective function is nonconvex. In fact, if we minimize a concave quadratic, no upper bound can be given as a function of n and Delta. Our key observation is that, in this setting, proximity phenomena still occur, but only if we consider also approximate solutions instead of optimal solutions only. In our main result we provide upper bounds on the distance between approximate (resp., optimal) solutions to a Concave integer quadratic programming problem and optimal (resp., approximate) solutions of its continuous relaxation. Our bounds are functions of n, Delta, and a parameter epsilon that controls the quality of the approximation. Furthermore, we discuss how far from optimal are our proximity bounds.
For a vector integer quadratic programming problem, a regularizing operator is proposed that acts on a vector criterion and transforms a possibly unstable initial problem into a series of perturbed stable problems wit...
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For a vector integer quadratic programming problem, a regularizing operator is proposed that acts on a vector criterion and transforms a possibly unstable initial problem into a series of perturbed stable problems with the same Pareto set. The technique of epsilon-regularization is developed that allows replacing the considered problem by perturbed epsilon-stable problems.
In this paper we introduce integer quadratic programming (MIQP) approach to optimally detect QPSK Code Spread OFDM (CS-OFDM) by formulating the problem as a combinatorial optimization problem. The Branch and Bound (BB...
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ISBN:
(纸本)9780819490827
In this paper we introduce integer quadratic programming (MIQP) approach to optimally detect QPSK Code Spread OFDM (CS-OFDM) by formulating the problem as a combinatorial optimization problem. The Branch and Bound (BB) algorithm is utilized to solve this integer quadratic programming problem. Furthermore, we propose combined preprocessing steps that can be applied prior to BB so that the computational complexity of the optimum receiver is reduced. The first step in this combination is to detect as much as possible symbols using procedures presented in [9], which is basically based on the gradient of quadratic function. The second step detects the undetected symbols from the first step using MMSE estimator. The result of the latter step will be used to predict the initial upper bound of the BB algorithm. Simulation results show that the proposed preprocessing combination when applied prior to BB provides optimal performance with a significantly reduced computational complexity.
In this paper we introduce integer quadratic programming (IQP) approach to detect QPSK Code Spread OFDM (CSOFDM) signal by formulating the problem as a combinatorial optimization problem. The Branch and Bound (BB) alg...
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ISBN:
(纸本)9781467350518
In this paper we introduce integer quadratic programming (IQP) approach to detect QPSK Code Spread OFDM (CSOFDM) signal by formulating the problem as a combinatorial optimization problem. The Branch and Bound (BB) algorithm is utilized to solve this integer quadratic programming problem. Furthermore, we propose preprocessing procedures that can be applied prior to BB so that the computational complexity of the optimum receiver is reduced. The basic idea of the proposed preprocessing is to introduce a good choice of upper bound for the BB search tree and/or reduce the search space of the BB problem. Performance and complexity computations of these preprocessing are investigated. Simulation results show that the proposed preprocessing when applied prior to BB provides optimal or near optimal performance with a significantly reduced computational complexity.
Alignment of protein-protein interfaces plays a key role in the studies of protein function,signal transduction network and drug *** give a protein-protein interface alignment method which is based on an integer quadr...
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Alignment of protein-protein interfaces plays a key role in the studies of protein function,signal transduction network and drug *** give a protein-protein interface alignment method which is based on an integer quadratic programming *** alignment method integrates sequence evolutionary information and structural information of proteins,and scores the aligned residues using the similarity of their evolutionary ***,we use the alignment method to identify evolutionally and structurally conserved *** the computational experiments,we show that those evolutionally and structurally conserved residues are likely to be the key residues for protein-protein interaction,*** spots.
Alignment of protein-protein interfaces plays a key role in the studies of protein function,signal transduction network and drug *** give a protein-protein interface alignment method which is based on an integer quadr...
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Alignment of protein-protein interfaces plays a key role in the studies of protein function,signal transduction network and drug *** give a protein-protein interface alignment method which is based on an integer quadratic programming *** alignment method integrates sequence evolutionary information and structural information of proteins,and scores the aligned residues using the similarity of their evolutionary ***,we use the alignment method to identify evolutionally and structurally conserved residues. Through the computational experiments,we show that those evolutionally and structurally conserved residues are likely to be the key residues for protein-protein interaction,*** spots.
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