Displaying similar documents to “The Perturbed Generalized Tikhonov's Algorithm”

Perturbed Proximal Point Algorithm with Nonquadratic Kernel

Brohe, M., Tossings, P. (2000)

Serdica Mathematical Journal

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Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R. T. Rockafellar [16], for solving the problem (P) ”To find x ∈ H such that 0 ∈ T x” is the proximal point algorithm. Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, . . . We summarize some of...

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...

Approximating solutions of split equality of some nonlinear optimization problems using an inertial algorithm

Lateef O. Jolaoso, Oluwatosin T. Mewomo (2020)

Commentationes Mathematicae Universitatis Carolinae

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This paper presents an inertial iterative algorithm for approximating a common solution of split equalities of generalized mixed equilibrium problem, monotone variational inclusion problem, variational inequality problem and common fixed point problem in real Hilbert spaces. The algorithm is designed in such a way that it does not require prior knowledge of the norms of the bounded linear operators. We prove a strong convergence theorem under some mild conditions of the control sequences...

Modified golden ratio algorithms for pseudomonotone equilibrium problems and variational inequalities

Lulu Yin, Hongwei Liu, Jun Yang (2022)

Applications of Mathematics

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We propose a modification of the golden ratio algorithm for solving pseudomonotone equilibrium problems with a Lipschitz-type condition in Hilbert spaces. A new non-monotone stepsize rule is used in the method. Without such an additional condition, the theorem of weak convergence is proved. Furthermore, with strongly pseudomonotone condition, the $R$-linear convergence rate of the method is established. The results obtained are applied to a variational inequality problem, and the convergence...

Numerical considerations of a hybrid proximal projection algorithm for solving variational inequalities

Christina Jager (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, some ideas for the numerical realization of the hybrid proximal projection algorithm from Solodov and Svaiter [22] are presented. An example is given which shows that this hybrid algorithm does not generate a Fejér-monotone sequence. Further, a strategy is suggested for the computation of inexact solutions of the auxiliary problems with a certain tolerance. For that purpose, ε-subdifferentials of the auxiliary functions and the bundle trust region method from Schramm and...

Kaczmarz algorithm with relaxation in Hilbert space

Ryszard Szwarc, Grzegorz Świderski (2013)

Studia Mathematica

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We study the relaxed Kaczmarz algorithm in Hilbert space. The connection with the non-relaxed algorithm is examined. In particular we give sufficient conditions when relaxation leads to the convergence of the algorithm independently of the relaxation coefficients.