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An Approximate, Efficient LP Solver for LP Rounding
Srikrishna Sridhar · Stephen Wright · Christopher Re · Ji Liu · Victor Bittorf · Ce Zhang

Thu Dec 05 07:00 PM -- 11:59 PM (PST) @ Harrah's Special Events Center, 2nd Floor

Many problems in machine learning can be solved by rounding the solution of an appropriate linear program. We propose a scheme that is based on a quadratic program relaxation which allows us to use parallel stochastic-coordinate-descent to approximately solve large linear programs efficiently. Our software is an order of magnitude faster than Cplex (a commercial linear programming solver) and yields similar solution quality. Our results include a novel perturbation analysis of a quadratic-penalty formulation of linear programming and a convergence result, which we use to derive running time and quality guarantees.

Author Information

Srikrishna Sridhar (UW-Madison)
Stephen Wright (UW-Madison)

Steve Wright is a Professor of Computer Sciences at the University of Wisconsin-Madison. His research interests lie in computational optimization and its applications to science and engineering. Prior to joining UW-Madison in 2001, Wright was a Senior Computer Scientist (1997-2001) and Computer Scientist (1990-1997) at Argonne National Laboratory, and Professor of Computer Science at the University of Chicago (2000-2001). He is the past Chair of the Mathematical Optimization Society (formerly the Mathematical Programming Society), the leading professional society in optimization, and a member of the Board of the Society for Industrial and Applied Mathematics (SIAM). Wright is the author or co-author of four widely used books in numerical optimization, including "Primal Dual Interior-Point Methods" (SIAM, 1997) and "Numerical Optimization" (with J. Nocedal, Second Edition, Springer, 2006). He has also authored over 85 refereed journal papers on optimization theory, algorithms, software, and applications. He is coauthor of widely used interior-point software for linear and quadratic optimization. His recent research includes algorithms, applications, and theory for sparse optimization (including applications in compressed sensing and machine learning).

Christopher Re (UW-Madison)
Ji Liu (Kwai Inc.)
Victor Bittorf (UW-Madison)
Ce Zhang (Wisconsin)

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