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Zbl 0890.90151
Teboulle, Marc
Convergence of proximal-like algorithms. (English)
[J] SIAM J. Optim. 7, No.4, 1069-1083 (1997). ISSN 1052-6234; ISSN 1095-7189/e

Summary: We analyze proximal methods based on entropy-like distances for the minimization of convex functions subject to nonnegativity constraints. We prove global convergence results for the methods with approximate minimization steps and an ergodic convergence result for the case of finding a zero of a maximal monotone operator. We also consider linearly constrained convex problems and establish a quadratic convergence rate result for linear programs. Our analysis allows us to simplify and extend the available convergence results for these methods.

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

Keywords: convex optimization; proximal methods; maximal monotone operator

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