Results 1  10
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390
A lifted linear programming branchandbound algorithm for mixed integer conic quadratic programs
, 2007
"... This paper develops a linear programming based branchandbound algorithm for mixed integer conic quadratic programs. The algorithm is based on a higher dimensional or lifted polyhedral relaxation of conic quadratic constraints introduced by BenTal and Nemirovski. The algorithm is different from o ..."
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Cited by 26 (1 self)
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This paper develops a linear programming based branchandbound algorithm for mixed integer conic quadratic programs. The algorithm is based on a higher dimensional or lifted polyhedral relaxation of conic quadratic constraints introduced by BenTal and Nemirovski. The algorithm is different from
Multiple kernel learning, conic duality, and the SMO algorithm
 In Proceedings of the 21st International Conference on Machine Learning (ICML
, 2004
"... While classical kernelbased classifiers are based on a single kernel, in practice it is often desirable to base classifiers on combinations of multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for the support vector machine (SVM), and showed that the optimiz ..."
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Cited by 445 (31 self)
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that the optimization of the coefficients of such a combination reduces to a convex optimization problem known as a quadraticallyconstrained quadratic program (QCQP). Unfortunately, current convex optimization toolboxes can solve this problem only for a small number of kernels and a small number of data points
Control of Systems Integrating Logic, Dynamics, and Constraints
 Automatica
, 1998
"... This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real and ..."
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Cited by 413 (50 self)
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reference trajectories while fulfilling operating constraints, and possibly take into account previous qualitative knowledge in the form of heuristic rules. Due to the presence of integer variables, the resulting online optimization procedures are solved through Mixed Integer Quadratic Programming (MIQP
Large scale multiple kernel learning
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2006
"... While classical kernelbased learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for classification, leading to a convex quadratically constrained quadratic program. We s ..."
Abstract

Cited by 340 (20 self)
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While classical kernelbased learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for classification, leading to a convex quadratically constrained quadratic program. We
Support vector machines for multipleinstance learning
 Advances in Neural Information Processing Systems 15
, 2003
"... This paper presents two new formulations of multipleinstance learning as a maximum margin problem. The proposed extensions of the Support Vector Machine (SVM) learning approach lead to mixed integer quadratic programs that can be solved heuristically. Our generalization of SVMs makes a stateofthe ..."
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Cited by 314 (2 self)
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This paper presents two new formulations of multipleinstance learning as a maximum margin problem. The proposed extensions of the Support Vector Machine (SVM) learning approach lead to mixed integer quadratic programs that can be solved heuristically. Our generalization of SVMs makes a state
Extended Formulations in Mixed Integer Conic Quadratic Programming
, 2015
"... In this paper we consider the use of extended formulations in LPbased algorithms for mixed integer conic quadratic programming (MICQP). Through an homogenization procedure we generalize an existing extended formulation to general conic quadratic constraints. We then compare its effectiveness again ..."
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In this paper we consider the use of extended formulations in LPbased algorithms for mixed integer conic quadratic programming (MICQP). Through an homogenization procedure we generalize an existing extended formulation to general conic quadratic constraints. We then compare its effectiveness
Autocalibration and the absolute quadric
 in Proc. IEEE Conf. Computer Vision, Pattern Recognition
, 1997
"... We describe a new method for camera autocalibration and scaled Euclidean structure and motion, from three or more views taken by a moving camera with fixed but unknown intrinsic parameters. The motion constancy of these is used to rectify an initial projective reconstruction. Euclidean scene structu ..."
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Cited by 248 (7 self)
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easily. The nonlinear method is stabler, faster, more accurate and more general than the quasilinear one. It is based on a general constrained optimization technique — sequential quadratic programming — that may well be useful in other vision problems.
Cuts for mixed 01 conic programming
, 2005
"... In this we paper we study techniques for generating valid convex constraints for mixed 01 conic programs. We show that many of the techniques developed for generating linear cuts for mixed 01 linear programs, such as the Gomory cuts, the liftandproject cuts, and cuts from other hierarchies of ti ..."
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Cited by 29 (0 self)
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of tighter relaxations, extend in a straightforward manner to mixed 01 conic programs. We also show that simple extensions of these techniques lead to methods for generating convex quadratic cuts. Gomory cuts for mixed 01 conic programs have interesting implications for comparing the semidefinite
On the copositive representation of binary and continuous nonconvex quadratic programs
, 2007
"... In this paper, we model any nonconvex quadratic program having a mix of binary and continuous variables as a linear program over the dual of the cone of copositive matrices. This result can be viewed as an extension of earlier separate results, which have established the copositive representation of ..."
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Cited by 89 (6 self)
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In this paper, we model any nonconvex quadratic program having a mix of binary and continuous variables as a linear program over the dual of the cone of copositive matrices. This result can be viewed as an extension of earlier separate results, which have established the copositive representation
Robust Solutions of Uncertain Quadratic and ConicQuadratic Problems
 Solutions of Uncertain Linear Programs: Math. Program
, 2001
"... We consider a conicquadratic (and in particular a quadratically constrained) optimization problem with uncertain data, known only to reside in some uncertainty set U . The robust counterpart of such a problem leads usually to an NPhard semidefinite problem; this is the case for example when U is g ..."
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Cited by 52 (8 self)
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We consider a conicquadratic (and in particular a quadratically constrained) optimization problem with uncertain data, known only to reside in some uncertainty set U . The robust counterpart of such a problem leads usually to an NPhard semidefinite problem; this is the case for example when U
Results 1  10
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390