Mathematical Programming

, Volume 173, Issue 1–2, pp 1–35 | Cite as

Accelerated first-order methods for hyperbolic programming

  • James RenegarEmail author
Full Length Paper Series A


We develop a framework 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. An iteration bound for a representative accelerated method is derived.


Hyperbolic programming Accelerated first-order methods Convex optimization 

Mathematics Subject Classification

90C25 90C22 


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Copyright information

© Springer-Verlag GmbH Germany and Mathematical Optimization Society 2017

Authors and Affiliations

  1. 1.School of Operations Research and Information EngineeringCornell UniversityIthacaUSA

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