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Zbl 0766.90071
Teboulle, Marc
Entropic proximal mappings with applications to nonlinear programming. (English)
[J] Math. Oper. Res. 17, No.3, 670-690 (1992). ISSN 1526-5471; ISSN 0364-765X/e

For a closed proper convex function $f$ and a given kernel $\psi$, the author introduces the entropic proximal mapping $E\sb \psi(f,z)$ as the unique optimizer of the problem $\inf\{f(x)+D\sb \psi(x,z),\ x\in R\sp n\}$, where $D\sb \psi(x,z)=\psi(x)-\psi(z)-(x-z)\sp T\nabla\psi(z)$ 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.
[J.Rohn (Praha)]

MSC 2000:: *90C30 Nonlinear programming
90C25 Convex programming

Keywords: entropic proximal mapping; smoothing properties; generalized augmented Lagrangians; modifier barrier functions

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