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Exact quadratic convex reformulations of mixed-integer quadratically constrained problems

MATHEMATICAL programming 2016年第1-2期158卷 235-266页

作者： Billionnet, Alain Elloumi, Sourour Lambert, Amelie CEDRIC ENSIIE 1 Sq Resistance F-91025 Evry France CEDRIC Cnam 292 Rue St Martin F-75141 Paris 03 France

We propose a solution approach for the general problem (QP) of minimizing a quadratic function of bounded integer variables subject to a set of quadratic constraints. The resolution is based on the reformulation of the original problem (QP) into an equivalent quadratic problem whose continuous relaxation is convex, so that it can be effectively solved by a branch-and-bound algorithm based on quadratic convex relaxation. We concentrate our efforts on finding a reformulation such that the continuous relaxation bound of the reformulated problem is as tight as possible. Furthermore, we extend our method to the case of mixed-integer quadratic problems with the following restriction: all quadratic sub-functions of purely continuous variables are already convex. Finally, we illustrate the different results of the article by small examples and we present some computational experiments on pure-integer and mixed-integer instances of (QP). Most of the considered instances with up to 53 variables can be solved by our approach combined with the use of Cplex.

关键词： integer quadratic programming Equivalent convex reformulation Semidefinite programming Branch-and-bound algorithm

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ACROSS: A Framework for Multi-Cultural Interlinking of Web Taxonomies 16

ACROSS: A Framework for Multi-Cultural Interlinking of Web T...

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8th ACM Web Science Conference (WebSci)

作者： Boldyrev, Natalia Spaniol, Marc Weikum, Gerhard Max Planck Inst Informat Saarbrucken Germany Univ Caen Normandie Caen France

ISBN: (纸本)9781450342087

The Web hosts a huge variety of multi-cultural taxonomies. They encompass product catalogs of e-commerce, general-purpose knowledge bases and numerous domain-specific category systems. The "common denominator" of all these is their enormous diversity, which makes it infeasible to combine multiple taxonomies for ad-hoc tasks. To support the alignment of independently created Web taxonomies, we introduce the ACROSS framework. For mapping categories across different taxonomies, ACROSS harnesses instance-level features as well as distant supervision from an intermediate source like multiple Wikipedia editions. Our experiments with heterogeneous taxonomies for different domains demonstrate the viability of our approach and improvement over state-of-the-art baselines.

关键词： Multicultural Knowledge Bases Knowledge Taxonomies Alignment Methods integer Linear programming integer quadratic programming Label Propagation

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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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A roof linearization algorithm to obtain a tight upper bound for integer nonseparable quadratic programming

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Electronic Notes in Discrete Mathematics 2010年第C期36卷 271-278页

作者： Quadri, Dominique Soutif, Éric Université d'Avignon et des Pays du Vaucluse LIA F-84911 Avignon Cedex 9 France CEDRIC-CNAM 292 rue Saint Martin 75141 Paris Cedex 03 France

We study in this paper a general case of integer quadratic multi-knapsack problem (QMKP) where the objective function is non separable. An upper bound is proposed for (QMKP) which is computed via two steps. We first rewrite (QMKP) into an equivalent separable mixed integer quadratic program (QP_x,y), using Gauss decomposition of the quadratic terms matrix. We then suggest an original technique, we call roof linearization, to linearize (QP_x,y) so as to obtain a mixed integer linear program which optimal value provides an upper bound for both (QP_x,y) and (QMKP). Preliminary computational experiments are conducted so as to assess that the proposed algorithm provides a tight upper bound in fast CPU times. © 2010 Elsevier B.V.

关键词： integer quadratic programming Knapsack problems Linearization techniques Non separable function

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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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From Angular Manifolds to the integer Lattice: Guaranteed Orientation Estimation With Application to Pose Graph Optimization

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IEEE TRANSACTIONS ON ROBOTICS 2014年第2期30卷 475-492页

作者： Carlone, Luca Censi, Andrea Georgia Inst Technol Coll Comp Atlanta GA 30332 USA MIT Informat & Decis Syst Lab Cambridge MA 02139 USA

Pose graph optimization from relative measurements is challenging because of the angular component of the poses: the variables live on a manifold product with nontrivial topology and the likelihood function is nonconvex and has many local minima. Because of these issues, iterative solvers are not robust to large amounts of noise. This paper describes a global estimation method, called multi-hypothesis orientation-from-lattice estimation in 2-D (MOLE2D), for the estimation of the nodes' orientation in a pose graph. We demonstrate that the original nonlinear optimization problem on the manifold product is equivalent to an unconstrained quadratic optimization problem on the integer lattice. Exploiting this insight, we show that, in general, the maximum likelihood estimate alone cannot be considered a reliable estimator. Therefore, MOLE2D returns a set of point estimates, for which we can derive precise probabilistic guarantees. Experiments show that the method is able to tolerate extreme amounts of noise, far above all noise levels of sensors used in applications. Using MOLE2D's output to bootstrap the initial guess of iterative pose graph optimization methods improves their robustness and makes them avoid local minima even for high levels of noise.

关键词： integer quadratic programming mobile robots multi-hypothesis estimation orientation estimation pose graph optimization simultaneous localization and mapping (SLAM) SO(2) manifold

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An integer linear programming approach for a class of bilinear integer programs

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OPERATIONS RESEARCH LETTERS 2014年第3期42卷 226-230页

作者： Hu, Wuhua Tay, Wee Peng Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

We propose an integer Linear programming (ILP) approach for solving integer programs with bilinear objectives and linear constraints. Our approach is based on finding upper and lower bounds for the integer ensembles in the bilinear objective function, and using the bounds to obtain a tight ILP reformulation of the original problem, which can then be solved efficiently. Numerical experiments suggest that the proposed approach outperforms a latest iterative ILP approach, with notable reductions in the average solution time. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Bilinear integer programming integer linear programming integer quadratic programming Binary binary linearization Binary integer linearization Bipartite graph

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L1 Norm Minimization approach to MIMO detector 8

L1 Norm Minimization approach to MIMO detector

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8th International Conference on Signal Processing and Communication Systems, (ICSPCS)

作者： Hashimoto, Yo Konishi, Katsumi Takahashi, Tomohiro Uruma, Kazunori Furukawa, Toshihiro Tokyo Univ Sci Tokyo 162 Japan Kogakuin Univ Tokyo 160 Japan

ISBN: (纸本)9781479952557

This paper deals with the quadrature amplitude modulation (QAM) problem for the multiple-input multiple-output (MIMO) channel. Based on the maximum likelihood estimation, the QAM detection problem is formulated as an integer quadratic programming, which is a combinatorial problem and difficult to obtain exact solutions. In order to overcome combinatorial difficulties, this paper formulates the QAM detection problem as the l(o) norm minimization problem and relaxes it into a quadratic programming with the l(1) norm regularization. Utilizing and modifying the forward-backward splitting (FOBOS) algorithm, a new QAM detection algorithm is proposed. This algorithm has a trade-off between the computational cost and the detection accuracy, which depends on a parameter of the algorithm. Numerical simulations show that the proposed algorithm works well and achieves a good detection performance with less computational cost comparing with the semidefinite relaxation (SDR) based algorithm.

关键词： MIMO communication integer programming minimisation numerical analysis quadratic programming quadrature amplitude modulation FOBOS algorithm L1 norm minimization approach MIMO detector QAM detection algorithm SDR based algorithm combinatorial problem computational cost detection accuracy forward-backward splitting algorithm integer quadratic programming maximum likelihood estimation multiple-input multiple-output channel numerical simulations semidefinite relaxation based algorithm Approximation algorithms Detectors MIMO Quadrature amplitude modulation Signal processing algorithms Signal to noise ratio Vectors Quadrature amplitude modulation quadratic programming multiple input multiple output systems maximum likelihood estimation Signal processing algorithms signal to noise ratios MIMO communication Approximation algorithms integer programming Numerical Analysis

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Robust Feature Point Matching With Sparse Model

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2014年第12期23卷 5175-5186页

作者： Jiang, Bo Tang, Jin Luo, Bin Lin, Liang Anhui Univ Sch Comp Sci & Technol Hefei 230026 Peoples R China Sun Yat Sen Univ Sch Adv Comp Guangzhou 510275 Guangdong Peoples R China

Feature point matching that incorporates pairwise constraints can be cast as an integer quadratic programming (IQP) problem. Since it is NP-hard, approximate methods are required. The optimal solution for IQP matching problem is discrete, binary, and thus sparse in nature. This motivates us to use sparse model for feature point matching problem. The main advantage of the proposed sparse feature point matching (SPM) method is that it generates sparse solution and thus naturally imposes the discrete mapping constraints approximately in the optimization process. Therefore, it can optimize the IQP matching problem in an approximate discrete domain. In addition, an efficient algorithm can be derived to solve SPM problem. Promising experimental results on both synthetic points sets matching and real-world image feature sets matching tasks show the effectiveness of the proposed feature point matching method.

关键词： Feature point matching integer quadratic programming nonnegative matrix factorization sparse model

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New formulations of the multiple sequence alignment problem

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OPTIMIZATION LETTERS 2011年第1期5卷 27-40页

作者： Arthanari, Thiru S. Hoai An Le Thi Paul Verlaine Univ Metz Lab Theoret & Appl Comp Sci UFR MIM F-57045 Metz France Univ Auckland Dept ISOM Auckland 1 New Zealand

A well known formulation of the multiple sequence alignment (MSA) problem is the maximum weight trace (MWT), a 0-1 linear programming problem. In this paper, we propose a new integer quadratic programming formulation of the MSA. The number of constraints and variables in the problem are only of the order of kL(2), where, k is the number of sequences and L is the total length of the sequences, that is, L = Sigma(k)(i=1) l(i), where l(i) is the length of sequence i. Based on this formulation we introduce an equivalent linear constrained 0-1 quadratic programming problem. We also propose a 0-1 linear programming formulation of the MWT problem, with polynomially many constraints. Our formulation provides the first direct compact formulation that ensures that the critical circuit inequalities (which are exponentially many) are all met.

关键词： Multiple sequence alignment (MSA) integer quadratic programming Linear constrained 0-1 quadratic programming Maximum weight trace (MWT) 0-1 Linear programming DC programming, DCA

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