Displaying similar documents to “An Extension of the Auxiliary Problem Principle to Nonsymmetric Auxiliary Operators”

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...

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...

Convergence results of iterative algorithms for the sum of two monotone operators in reflexive Banach spaces

Yan Tang, Ratthaprom Promkam, Prasit Cholamjiak, Pongsakorn Sunthrayuth (2022)

Applications of Mathematics

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The aim of this paper is to propose two modified forward-backward splitting algorithms for zeros of the sum of a maximal monotone operator and a Bregman inverse strongly monotone operator in reflexive Banach spaces. We prove weak and strong convergence theorems of the generated sequences by the proposed methods under some suitable conditions. We apply our results to study the variational inequality problem and the equilibrium problem. Finally, a numerical example is given to illustrate...

Plurisubharmonic functions on compact sets

Rafał Czyż, Lisa Hed, Håkan Persson (2012)

Annales Polonici Mathematici

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Poletsky has introduced a notion of plurisubharmonicity for functions defined on compact sets in ℂⁿ. We show that these functions can be completely characterized in terms of monotone convergence of plurisubharmonic functions defined on neighborhoods of the compact.