Accelerated first-order methods for hyperbolic programming

• 成果类型: Article
• 署名作者: Renegar, James
• 署名单位: Cornell University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1203-y
• 发表日期: 2019
• 页码: 1-35
• 关键词: Polynomials; INEQUALITY

摘要

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.