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Mixed-type reverse order law and its equivalents

Nebojša Č. Dinčić, Dragan S. Djordjević, Dijana Mosić (2011)

Studia Mathematica

We present new results related to various equivalents of the mixed-type reverse order law for the Moore-Penrose inverse for operators on Hilbert spaces. Recent finite-dimensional results of Tian are extended to Hilbert space operators.

Modified golden ratio algorithms for pseudomonotone equilibrium problems and variational inequalities

Lulu Yin, Hongwei Liu, Jun Yang (2022)

Applications of Mathematics

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 rate...

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