Prox-PEP achieves O(T^{-1/4}) expected oracle complexity for epsilon-KKT stationarity in weakly convex stochastic nonlinear programming via proximal steps, exact penalty, and designed quadratic subproblems.
Xiao, Dual averaging methods for regularized stochastic learning and online optimization, Journal of Machine Learning Research, 11 (2010), 2543–2596
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PMQSopt achieves expected O(T^{-1/4}) convergence rates for three epsilon-KKT metrics after T iterations in weakly convex stochastic programming under weak convexity and strict feasibility assumptions.
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Prox-PEP: A Proximal Partial Exact Penalty Algorithm for Weakly Convex Stochastic Nonlinear Programming
Prox-PEP achieves O(T^{-1/4}) expected oracle complexity for epsilon-KKT stationarity in weakly convex stochastic nonlinear programming via proximal steps, exact penalty, and designed quadratic subproblems.
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A Quadratic-Approximation-Based Stochastic Approximation Method for Weakly Convex Stochastic Programming
PMQSopt achieves expected O(T^{-1/4}) convergence rates for three epsilon-KKT metrics after T iterations in weakly convex stochastic programming under weak convexity and strict feasibility assumptions.