fixed point theory – Optimization Online

Convergence Results for Primal-Dual Algorithms in the Presence of Adjoint Mismatch

Published: 2022/04/17

Convex Optimization, Nonsmooth Optimization adjoint mismatch, convergence analysis, convex optimization, CT reconstruction, fixed point theory, forward-backward splitting, primal-dual algorithms, Tseng’s splitting

Most optimization problems arising in imaging science involve high-dimensional linear operators and their adjoints. In the implementations of these operators, approximations may be introduced for various practical considerations (e.g., memory limitation, computational cost, convergence speed), leading to an adjoint mismatch. This occurs for the X-ray tomographic inverse problems found in Computed Tomography (CT), where the … Read more

Fixed points and variational principles with applications to capability theory of wellbeing via variational rationality

Published: 2014/03/31

Boris S. Mordukhovich

Antoine Soubeyran

Bao Q. Truong

Applications - OR and Management Sciences, Multi-Criteria Optimization, Nonsmooth Optimization capacity approach to wellbeing, fixed point theory, variational analysis and optimization, variational principles, variational rationality

In this paper we first develop two new results of variational analysis. One is a fixed point theorem for parametric dynamic systems in quasimetric spaces, which can also be interpreted as an existence theorem of minimal points with respect to reflexive and transitive preferences for sets in products spaces. The other one is a variational … Read more