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Computing efficient exact designs of experiments using integer quadratic programming

COMPUTATIONAL STATISTICS & DATA ANALYSIS 2014年 71卷 1159-1167页

作者： Harman, Radoslav Filova, Lenka Comenius Univ Fac Math Phys & Informat Dept Appl Math & Stat Bratislava 84248 Slovakia

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.

关键词： D-optimal design DQ-optimal design Exact design Marginal constraints Cost constraints integer quadratic programming

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EXACT AUGMENTED LAGRANGIAN DUALITY FOR MIXED integer quadratic programming

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SIAM JOURNAL ON OPTIMIZATION 2020年第1期30卷 781-797页

作者： Gu, Xiaoyi Ahmed, Shabbir Dey, Santanu S. Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA

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.

关键词： augmented Lagrangian integer quadratic programming strong dual

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Reducing the number of variables in integer quadratic programming problem

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APPLIED MATHEMATICAL MODELLING 2010年第2期34卷 424-436页

作者： Zhou MinJin Chen Wei Shanghai Univ Dept Math Shanghai Peoples R China

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.

关键词： integer quadratic programming Variable reduction Separable integer quadratic programming

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SUBDETERMINANTS AND CONCAVE integer quadratic programming

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SIAM JOURNAL ON OPTIMIZATION 2019年第4期29卷 3154-3173页

作者： Del Pia, Alberto Univ Wisconsin Dept Ind & Syst Engn Madison WI 53706 USA Univ Wisconsin Wisconsin Inst Discovery Madison WI 53706 USA

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.

关键词： integer quadratic programming approximation algorithm concave function subdeterminants total unimodularity total bimodularity

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Proximity in concave integer quadratic programming

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MATHEMATICAL programming 2022年第1-2期194卷 871-900页

作者： Del Pia, Alberto Ma, Mingchen Univ Wisconsin Dept Ind & Syst Engn Madison WI USA Univ Wisconsin Wisconsin Inst Discovery Madison WI USA Univ Wisconsin Dept Comp Sci Madison WI 53706 USA

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.

关键词： integer quadratic programming quadratic programming Concave minimization Proximity Sensitivity subdeterminants

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ON THE REGULARIZATION OF VECTOR integer quadratic programming PROBLEMS

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CYBERNETICS AND SYSTEMS ANALYSIS 2009年第2期45卷 274-280页

作者： Emeliehev, V. A. Gurevskii, E. E. Bclarusian State Univ Minsk BELARUS

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.

关键词： multicriteriality integer quadratic programming Pareto set stability stabilization regularization epsilon-stabilization epsilon-regularization

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Detection of Code Spread OFDM Based on 0-1 integer quadratic programming

Detection of Code Spread OFDM Based on 0-1 Integer Quadratic...

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Conference on Wireless Sensing, Localization and Processing VII

作者： Elghariani, Ali Zoltowski, Michael D. Purdue Univ Sch Elect & Comp Engn W Lafayette IN 47907 USA

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.

关键词： CSOFDM integer quadratic programming Branch and Bound MMSE Computational complexity

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Detection of Code Spread OFDM Based on 0-1 integer quadratic programming

Detection of Code Spread OFDM Based on 0-1 Integer Quadratic...

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46th Asilomar Conference on Signals, Systems and Computers

作者： Elghariani, Ali Zoltowski, Michael D. Purdue Univ Sch Elect & Comp Engn W Lafayette IN 47907 USA

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.

关键词： CSOFDM integer quadratic programming Branch and Bound MMSE LLR Computational complexity

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Alignment of protein-protein interfaces by integer quadratic programming

Alignment of protein-protein interfaces by integer quadratic...

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2010 International Conference on Services Science, Management and Engineering (SSME 2010)

作者： Wen-Juan Zhang Department of Basic Courses Tianjin Foreign Studies University Tianjin,China Lin Wang Computer Science and Information Engineering College Tianjin University of Science and Technology Tianjin,China

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.

关键词： protein interface alignment hot spot integer quadratic programming

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Alignment of Protein-Protein Interfaces by integer quadratic programming

Alignment of Protein-Protein Interfaces by Integer Quadratic...

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2012 International Conference on Convergence Computer Technology(IC3T 2012)

作者： Wen-Juan Zhang Lin Wang Department of Basic Courses Tianjin Foreign Studies University Tianjin China Computer Science and Information Engineering College Tianjin University of Science and Technology

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.

关键词： Protein interface alignment Hot spot integer quadratic programming

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