A Study of Convex Convex-Composite Functions via Infimal Convolution with Applications

• 成果类型: Article
• 署名作者: Burke, James, V; Tim, Hoheisel; Nguyen, Quang, V
• 署名单位: University of Washington; University of Washington Seattle; McGill University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2020.1099
• 发表日期: 2021
• 页码: 1324-1348
• 关键词: constraint qualification; optimality conditions; Sufficient conditions; variational analysis; pointwise maximum; optimization; conjugate; 2ND-ORDER; mappings

摘要

In this paper, we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone convexity, is straightforward. The results are established under a verifiable Slater-type condition, with relaxed monotonicity and without lower semi continuity assumptions on the functions in play. The versatility of our findings is illustrated by a series of applications in optimization and matrix analysis, including conic programming, matrix-fractional, variational Gram, and spectral functions.