Ghost Penalties in Nonconvex Constrained Optimization: Diminishing Stepsizes and Iteration Complexity

• 成果类型: Article
• 署名作者: Facchinei, Francisco; Kungurtsev, Vyacheslav; Lampariello, Lorenzo; Scutari, Gesualdo
• 署名单位: Sapienza University Rome; Czech Technical University Prague; Roma Tre University; Purdue University System; Purdue University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2020.1079
• 发表日期: 2021
• 页码: 595-627
• 关键词: quadratic-programming algorithm; cubic regularization; distributed methods; GLOBAL CONVERGENCE; Newton method; minimization; convex; parallel; MODEL; EQUALITY

摘要

We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. We make use of classical penalty functions in an unconventional way, in that penalty functions only enter in the theoretical analysis of convergence while the algorithm itself is penalty free. Based on this idea, we are able to establish several new results, including the first general analysis for diminishing stepsize methods in nonconvex, constrained optimization, showing convergence to generalized stationary points, and a complexity study for sequential quadratic programming-type algorithms.