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

Author

Listed:
  • 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)

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.

Suggested Citation

  • James V. Burke & Hoheisel Tim & Quang V. Nguyen, 2021. "A Study of Convex Convex-Composite Functions via Infimal Convolution with Applications," Mathematics of Operations Research, INFORMS, vol. 46(4), pages 1324-1348, November.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:4:p:1324-1348
    DOI: 10.1287/moor.2020.1099
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