Golden ratio algorithms for variational inequalities Article Swipe

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Mathematics Variational inequality Iterated function Lipschitz continuity Monotone polygon Ergodic theory Rate of convergence Fixed point Operator (biology) Convergence (economics) Algorithm Strongly monotone Applied mathematics Mathematical analysis Computer science Geometry Computer network Repressor Economics Gene Biochemistry Channel (broadcasting) Chemistry Transcription factor Economic growth

Yura Malitsky ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.1007/s10107-019-01416-w · OA: W2965900084

The paper presents a fully adaptive algorithm for monotone variational inequalities. In each iteration the method uses two previous iterates for an approximation of the local Lipschitz constant without running a linesearch. Thus, every iteration of the method requires only one evaluation of a monotone operator F and a proximal mapping g. The operator F need not be Lipschitz continuous, which also makes the algorithm interesting in the area of composite minimization. The method exhibits an ergodic O(1 / k) convergence rate and R-linear rate under an error bound condition. We discuss possible applications of the method to fixed point problems as well as its different generalizations.