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

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 cone convexity, is straightforward. The results are established under verifiable Slater-type condition, with relaxed monotonicity without lower semicontinuity assumptions the play. versatility of our findings illustrated by series applications optimization matrix analysis, including conic programming, matrix-fractional, variational Gram, spectral functions.