Partial smoothness and constant rank

2018/07/09 by Adrian S. Lewis, Lewis, Adrian S., Jingwei Liang +1 · 2 citations
Computer Science · Mathematics · #49M05 #65K10 #90C31 #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1807.03134

openalex publication_date 2018/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The idea of partial smoothness in optimization blends certain smooth and nonsmooth properties of feasible regions and objective functions. As a consequence, the standard first-order conditions guarantee that diverse iterative algorithms (and post-optimality analyses) identify active structure or constraints. However, by instead focusing directly on the first-order conditions, the formal concept of partial smoothness simplifies dramatically: in basic differential geometric language, it is just a constant-rank condition. In this view, partial smoothness extends to more general mappings, such as saddlepoint operators underlying primal-dual splitting algorithms.

Cited by

• SSNCVX: A primal-dual semismooth Newton method for convex composite optimization problem
• LeAP-SSN: A Semismooth Newton Method with Global Convergence Rates

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