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About: Proximal operator     Goto   Sponge   NotDistinct   Permalink

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In mathematical optimization, the proximal operator is an operator associated with a proper, lower semi-continuous convex function from a Hilbert space to , and is defined by: For any function in this class, the minimizer of the right-hand side above is unique, hence making the proximal operator well-defined. The of a function enjoys several useful properties for optimization, enumerated below. Note that all of these items require to be proper (i.e. not identically , and never take a value of ), convex, and lower semi-continuous.