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Proximity Operators of Perspective Functions with Nonlinear Scaling
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A perspective function is a construction which combines a base function defined on a given space with a nonlinear scaling function defined on another space and which yields a lower semicontinuous convex function on the product space. Since perspective functions are typically nonsmooth, their use in first-order algorithms necessitates the computation of their proximity operator. This paper establishes closed-form expressions for the proximity operator of a perspective function defined on a Hilbert space in terms of a proximity operator involving its base function and one involving its scaling function.
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Cited by 2 Pith papers
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Projection onto cones generated by epigraphs of perspective functions
Projection onto the epigraph of the perspective of any convex lower semicontinuous function reduces to solving two scalar equations involving that function's proximity operator.
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