A Study of Convex Convex-Composite Functions via Infimal Convolution with Applications
A Study of Convex Convex-Composite Functions via Infimal Convolution with Applications
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DOI：
10.1287/moor.2020.1099
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发表时间：
2019-07
期刊：
影响因子：
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通讯作者：
J. Burke;Tim Hoheisel;Q. Nguyen
中科院分区：
文献类型：
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作者：
J. Burke;Tim Hoheisel;Q. Nguyen
本文给出了有限维空间中凸-凸复合函数的完全共轭性和次微分学。我们的方法，基于无穷卷积和锥凸性，是直接的。结果是建立在一个可验证的斯莱特型条件下，放松单调性，没有较低的连续性假设的功能在发挥作用。我们的研究结果的多功能性说明了一系列的应用程序在优化和矩阵分析，包括圆锥规划，矩阵分数，变分革兰氏，谱函数。
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 semicontinuity 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.