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

James V. Burke (), Hoheisel Tim () and Quang V. Nguyen ()
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James V. Burke: Department of Mathematics, University of Washington, Seattle, Washington 98115
Hoheisel Tim: Department of Mathematics and Statistics, McGill University, Montréal, Québec H3A 0B9, Canada
Quang V. Nguyen: Department of Mathematics and Statistics, McGill University, Montréal, Québec H3A 0B9, Canada

Mathematics of Operations Research, 2021, vol. 46, issue 4, 1324-1348

Abstract: 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.

Keywords: Primary: 52A41; 65K10; 90C25; 90C46; Primary: mathematics/convexity/matrices/programming/nondifferentiable/nonlinear; convex-composite function; cone-induced ordering; K -convexity; Fenchel conjugate; infimal convolution; subdifferential; conic programming; matrix-fractional function; variational Gram function; spectral function (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:46:y:2021:i:4:p:1324-1348

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