Computing the resolvent of composite operators
Copyright policy )Computing the resolvent of composite operators
Summary: Based in a very recent paper by \textit{C. A. Micchelli} et al. [Adv. Comput. Math. 38, No. 2, 401--426 (2013; Zbl 1275.65014)], we present an algorithmic approach for computing the resolvent of composite operators: the composition of a monotone operator and a continuous linear mapping. The proposed algorithm can be used, for example, for solving problems arising in image processing and traffic equilibrium. Furthermore, our algorithm gives an alternative to Dykstra-like method for evaluating the resolvent of the sum of two maximal monotone operators.
- UNIVERSITE D'AIX MARSEILLE France
- Université de Toulon France
- Laboratoire d'informatique et des systèmes France
- French National Centre for Scientific Research France
- University of Maine United States
Numerical optimization and variational techniques, Convex programming, Numerical methods based on nonlinear programming, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH] Mathematics [math], KM-algorithm, Yosida regularization, Douglas-Rachford algorithm, Iterative procedures involving nonlinear operators, maximal monotone operators, Dykstra-like method, Set-valued and variational analysis
Numerical optimization and variational techniques, Convex programming, Numerical methods based on nonlinear programming, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH] Mathematics [math], KM-algorithm, Yosida regularization, Douglas-Rachford algorithm, Iterative procedures involving nonlinear operators, maximal monotone operators, Dykstra-like method, Set-valued and variational analysis
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