A SPLITTING METHOD FOR COMPOSITE MAPPINGS

DOI10.1081/NFA-120016274zbMath1054.49022OpenAlexW2013632520MaRDI QIDQ4806006

Teemu Pennanen

Publication date: 2002

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/nfa-120016274

zbMATH Keywords

stochastic programmingvariational inequalitiesparameter estimationHilbert spaceset-valued mappingsplitting methodvariational inclusionsnonlinear partial differential equations in divergence form

Mathematics Subject Classification ID

Variational inequalities (49J40) Stochastic programming (90C15) Set-valued and variational analysis (49J53) Iterative procedures involving nonlinear operators (47J25) Theoretical approximation in context of PDEs (35A35)

Related Items

Unnamed Item, A class of Dantzig-Wolfe type decomposition methods for variational inequality problems, A primal-dual method of partial inverses for composite inclusions, A class of decomposition methods for convex optimization and monotone variational inclusions via the hybrid inexact proximal point framework, The hybrid proximal decomposition method applied to the computation of a Nash equilibrium for hydrothermal electricity markets, Solving monotone inclusions via compositions of nonexpansive averaged operators, A splitting method for stochastic programs, A variable metric proximal-descent algorithm for monotone operators, On an iterative method for finding a zero to the sum of two maximal monotone operators, An LS-free splitting method for composite mappings

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Partial inverse of a monotone operator
• On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
• Duality and optimality in multistage stochastic programming
• Composition duality and maximal monotonicity
• Variational composition of a monotone operator and a linear mapping with applications to elliptic PDEs with singular coefficients
• Applications of a Splitting Algorithm to Decomposition in Convex Programming and Variational Inequalities
• Quantitative Stability of Variational Systems: I. The Epigraphical Distance
• Monotone Operators and the Proximal Point Algorithm
• Generalized equations and their solutions, Part I: Basic theory
• Quantitative stability analysis for maximal monotone operators and semi-groups of contractions
• Convergence Rates in Forward--Backward Splitting
• Variational Analysis
• Operator-Splitting Methods for Monotone Affine Variational Inequalities, with a Parallel Application to Optimal Control
• Dualization of Generalized Equations of Maximal Monotone Type
• A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings
• Convex Analysis