Results 1 - 10 of 390

A lifted linear programming branch-and-bound algorithm for mixed integer conic quadratic programs

by Juan Pablo Vielma, Shabbir Ahmed, George L. Nemhauser , 2007
"... This paper develops a linear programming based branch-and-bound algorithm for mixed in-teger conic quadratic programs. The algorithm is based on a higher dimensional or lifted polyhedral relaxation of conic quadratic constraints introduced by Ben-Tal and Nemirovski. The algorithm is different from o ..."
Abstract - Cited by 26 (1 self) - Add to MetaCart
This paper develops a linear programming based branch-and-bound algorithm for mixed in-teger conic quadratic programs. The algorithm is based on a higher dimensional or lifted polyhedral relaxation of conic quadratic constraints introduced by Ben-Tal and Nemirovski. The algorithm is different from

Multiple kernel learning, conic duality, and the SMO algorithm

by Francis R. Bach, Gert R. G. Lanckriet - In Proceedings of the 21st International Conference on Machine Learning (ICML , 2004
"... While classical kernel-based 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 ..."
Abstract - Cited by 445 (31 self) - Add to MetaCart
that the optimization of the coefficients of such a combination reduces to a convex optimization problem known as a quadratically-constrained 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

by Alberto Bemporad, Manfred Morari - 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 ..."
Abstract - Cited by 413 (50 self) - Add to MetaCart
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 on-line optimization procedures are solved through Mixed Integer Quadratic Programming (MIQP

Large scale multiple kernel learning

by Sören Sonnenburg, Gunnar Rätsch , Christin Schäfer, Bernhard Schölkopf - JOURNAL OF MACHINE LEARNING RESEARCH , 2006
"... While classical kernel-based 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) - Add to MetaCart
While classical kernel-based 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 multiple-instance learning

by Stuart Andrews, Ioannis Tsochantaridis, Thomas Hofmann - Advances in Neural Information Processing Systems 15 , 2003
"... This paper presents two new formulations of multiple-instance 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-of-the ..."
Abstract - Cited by 314 (2 self) - Add to MetaCart
This paper presents two new formulations of multiple-instance 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

by Juan Pablo Vielma, Iain Dunning, Joey Huchette, et al. , 2015
"... In this paper we consider the use of extended formulations in LP-based 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 ..."
Abstract - Add to MetaCart
In this paper we consider the use of extended formulations in LP-based 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

by Bill Triggs - 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 ..."
Abstract - Cited by 248 (7 self) - Add to MetaCart
easily. The nonlinear method is stabler, faster, more accurate and more general than the quasi-linear 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 0-1 conic programming

by M. T. Cezik, et al. , 2005
"... In this we paper we study techniques for generating valid convex constraints for mixed 0-1 conic programs. We show that many of the techniques developed for generating linear cuts for mixed 0-1 linear programs, such as the Gomory cuts, the lift-and-project cuts, and cuts from other hierarchies of ti ..."
Abstract - Cited by 29 (0 self) - Add to MetaCart
of tighter relaxations, extend in a straightforward manner to mixed 0-1 conic programs. We also show that simple extensions of these techniques lead to methods for generating convex quadratic cuts. Gomory cuts for mixed 0-1 conic programs have interesting implications for comparing the semidefinite

On the copositive representation of binary and continuous nonconvex quadratic programs

by Samuel Burer , 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 ..."
Abstract - Cited by 89 (6 self) - Add to MetaCart
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 Conic-Quadratic Problems

by A. Ben-tal, A. Nemirovski, C. Roos - Solutions of Uncertain Linear Programs: Math. Program , 2001
"... We consider a conic-quadratic (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 NP-hard semidefinite problem; this is the case for example when U is g ..."
Abstract - Cited by 52 (8 self) - Add to MetaCart
We consider a conic-quadratic (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 NP-hard semidefinite problem; this is the case for example when U
Results 1 - 10 of 390