On the Softplus Penalty for Constrained Convex Optimization

2023/05/21 by Meng Li, Li, Meng, Paul Grigas +3
Computer Science · Engineering · Neuroscience · #FOS: Mathematics #Neuroinflammation and Neurodegeneration Mechanisms #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2305.12603

openalex publication_date 2023/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a new penalty reformulation of constrained convex optimization based on the softplus penalty function. We develop novel and tight upper bounds on the objective value gap and the violation of constraints for the solutions to the penalty reformulations by analyzing the solution path of the reformulation with respect to the smoothness parameter. We use these upper bounds to analyze the complexity of applying gradient methods, which are advantageous when the number of constraints is large, to the reformulation.

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