Proximal point method and elliptic regularization

DOI10.1016/j.na.2009.03.010zbMath1214.47062OpenAlexW2106078915MaRDI QIDQ838049

Rainer Tichatschke, Alexander Kaplan

Publication date: 21 August 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.03.010

zbMATH Keywords

maximal monotone operatorsvariational inequalitiesconvection-diffusion problemproximal point algorithmselliptic regularizationelasticity theoryminimal surface problem

Mathematics Subject Classification ID

Convex programming (90C25) Variational and other types of inequalities involving nonlinear operators (general) (47J20) Numerical optimization and variational techniques (65K10) Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (3)

Iterative Methods for the Elastography Inverse Problem of Locating Tumors ⋮ Interior proximal methods for quasiconvex optimization ⋮ Proximal Methods for the Elastography Inverse Problem of Tumor Identification Using an Equation Error Approach

Cites Work

• Construction of inertial manifolds by elliptic regularization
• Monotone (nonlinear) operators in Hilbert space
• Penalization in non-classical convex programming via variational convergence
• Solution of variational inequalities in mechanics
• Prox-regularization and solution of ill-posed elliptic variational inequalities
• Optimal control of the convection-diffusion equation using stabilized finite element methods
• Convergence of convex sets and of solutions of variational inequalities
• On existence and smoothness of solutions of some non-coercive variational inequalities
• Proximal Point Approach and Approximation of Variational Inequalities
• Proximal interior point method for convex semi-infinite programming
• Asymptotic Convergence Analysis of the Proximal Point Algorithm
• Combined Primal–Dual and Penalty Methods for Convex Programming
• Monotone Operators and the Proximal Point Algorithm
• On the Maximality of Sums of Nonlinear Monotone Operators
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