Displaying similar documents to “Perturbed Proximal Point Algorithm with Nonquadratic Kernel”

The Perturbed Generalized Tikhonov's Algorithm

Alexandre, P. (1999)

Serdica Mathematical Journal

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We work on the research of a zero of a maximal monotone operator on a real Hilbert space. Following the recent progress made in the context of the proximal point algorithm devoted to this problem, we introduce simultaneously a variable metric and a kind of relaxation in the perturbed Tikhonov’s algorithm studied by P. Tossings. So, we are led to work in the context of the variational convergence theory.

A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function

Pang, Li-Ping, Xia, Zun-Quan (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 90C25, 68W10, 49M37. A general framework of the (parallel variable transformation) PVT-type algorithm, called the PVT-MYR algorithm, for minimizing a non-smooth convex function is proposed, via the Moreau-Yosida regularization. As a particular scheme of this framework an ε-scheme is also presented. The global convergence of this algorithm is given under the assumptions of strong convexity of the objective function and an ε-descent...

An Extension of the Auxiliary Problem Principle to Nonsymmetric Auxiliary Operators

A. Renaud, G. Cohen (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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To find a zero of a maximal monotone operator, an extension of the Auxiliary Problem Principle to nonsymmetric auxiliary operators is proposed. The main convergence result supposes a relationship between the main operator and the nonsymmetric component of the auxiliary operator. When applied to the particular case of convex-concave functions, this result implies the convergence of the parallel version of the Arrow-Hurwicz algorithm under the assumptions of Lipschitz and partial...