Lagrange optimality system for a class of nonsmooth convex optimization
作者： B. Jin , T. Takeuchi
DOI: 10.1080/02331934.2015.1101598
关键词:
摘要: In this paper, we revisit the augmented Lagrangian method for a class of nonsmooth convex optimization. We present Lagrange optimality system associated with problems, and establish its connections standard condition saddle point Lagrangian, which provides powerful tool developing numerical algorithms: derive Lagrange–Newton algorithm optimization, nonsingularity Newton local convergence algorithm.
core.ac.uk
harvard.edu
sci-hub.se 参考文章(29)
Patrick L. Combettes, Heinz H. Bauschke, Convex Analysis and Monotone Operator Theory in Hilbert Spaces ,(2011)
Kazufumi Ito, Bangti Jin, None, Inverse Problems: Tikhonov Theory And Algorithms ,(2014)
Alberto Bemporad, Lorenzo Stella, Panagiotis Patrinos, Forward-backward truncated Newton methods for convex composite optimization arXiv: Optimization and Control. ,(2014)
Francisco Facchinei, Jong-Shi Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems ,(2003)
Tony F. Chan, Jianhong (Jackie) Shen, Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods. ,(2005) , 10.1137/1.9780898717877
Kazufumi Ito, Karl Kunisch, Lagrange Multiplier Approach to Variational Problems and Applications ,(2008)
LawrenceCraig Evans, Measure theory and fine properties of functions ,(1992)
Ivar Ekeland, Roger Téman, Convex analysis and variational problems ,(1976)
Maïtine Bergounioux, Kazufumi Ito, Karl Kunisch, Primal-Dual Strategy for Constrained Optimal Control Problems Siam Journal on Control and Optimization. ,vol. 37, pp. 1176- 1194 ,(1999) , 10.1137/S0363012997328609
Kazufumi Ito, Karl Kunisch, An active set strategy based on the augmented Lagrangian formulation for image restoration Mathematical Modelling and Numerical Analysis. ,vol. 33, pp. 1- 21 ,(1999) , 10.1051/M2AN:1999102