Linear Convergence of the Proximal Point Algorithm for Finding Solutions of Structured Convex Optimization Problems in Hilbert Spaces.
Abstract
The aim of this research to prove that the linear convergence towards an optimal solution to a structured convex optimization problem in real infinite dimensional Hilbert spaces is in good agreement with the proximal point algorithm. As we show that the proximal point algorithm which is an iterative procedure produces a sequence of better a pproximations to the fixed point of the resolvent operator. And we prove that this sequence is bounded and converges globally towards an optimal solution to the problem of structured convex optimizations and we also prove linear convergence towards the optimal solution of the problem.
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