Enhanced Computation of the Proximity Operator for Perspective Functions

Luis M. Briceño-Arias () and Cristóbal Vivar-Vargas ()
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Luis M. Briceño-Arias: Universidad Técnica Federico Santa María
Cristóbal Vivar-Vargas: Universidad Técnica Federico Santa María

Journal of Optimization Theory and Applications, 2024, vol. 200, issue 3, No 7, 1078-1099

Abstract: Abstract In this paper, we provide an explicit expression for the proximity operator of a perspective of any proper lower semicontinuous convex function defined on a Hilbert space. Our computation enhances and generalizes known formulae for the case when the Fenchel conjugate of the convex function has an open domain or when it is radial. We show numerically that our approach is more efficient than previous approaches in the literature and we provide several examples of nonradial functions for which the domain of its conjugate is not open and we compute the proximity operators of their perspectives.

Keywords: Convex analysis; Fenchel conjugate; Perspective function; Proximity operator; Recession function; 46N10; 47J20; 49J53; 49N15; 90C25 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02361-7

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