# A study of convex convex-composite functions via infimal convolution with applications

arXiv: https://arxiv.org/abs/1907.08318 · HTML: https://mlsanity.com/paper/1907.08318/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2019.

## Built on by (most cited first, 3 of 3)

- [Linearization Algorithms for Fully Composite Optimization](https://mlsanity.com/paper/2302.12808/) (2023)
- [Consistent Approximations in Composite Optimization](https://mlsanity.com/paper/2201.05250/) (2022)
- [On the Computational and Statistical Efficiency of the Empirical Maximum Entropy on the Mean Method](https://mlsanity.com/paper/2608.27705/) (2026)

## Abstract (arXiv)

In this note 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 and yields the desired results 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.