Accelerated First-Order Methods for Hyperbolic Programming

James Renegar (renegarcornell.edu)

Abstract: A framework is developed for applying accelerated methods to general hyperbolic programming, including linear, second-order cone, and semidefinite programming as special cases. The approach replaces a hyperbolic program with a convex optimization problem whose smooth objective function is explicit, and for which the only constraints are linear equations (one more linear equation than for the original problem). Virtually any first-order method can be applied. Iteration bounds for a representative accelerated method are derived.

Keywords: hyperbolic programming, accelerated gradient methods

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: arXiv:1512.07569

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Entry Submitted: 12/23/2015
Entry Accepted: 12/24/2015
Entry Last Modified: 12/26/2015

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