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Entropic proximal mappings with applications to nonlinear programming. (English) Zbl 0766.90071
For a closed proper convex function f and a given kernel ψ, the author introduces the entropic proximal mapping E ψ (f,z) as the unique optimizer of the problem inf{f(x)+D ψ (x,z),xR n }, where D ψ (x,z)=ψ(x)-ψ(z)-(x-z) T ψ(z) is the Bregman distance. A Moreau-type theorem as well as some smoothing properties are proved and applications for the construction of generalized augmented Lagrangians and modifier barrier functions are given.
Reviewer: J.Rohn (Praha)
MSC:
90C30Nonlinear programming
90C25Convex programming