Relax-and-split method for nonconvex inverse problems

[1]  M. Hestenes,et al.  Methods of conjugate gradients for solving linear systems , 1952 .

[2]  Richard Bellman,et al.  ON A ROUTING PROBLEM , 1958 .

[3]  R. Gerchberg.  A practical algorithm for the determination of phase from image and diffraction plane pictures , 1972 .

[4]  H. A. Ferwerda,et al.  The Problem of Phase Retrieval in Light and Electron Microscopy of Strong Objects: II. On the unique , 1976 .

[5]  丸山 徹.  Convex Analysisの二,三の進展について , 1977 .

[6]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[7]  L. Cromme.  Strong uniqueness , 1978 .

[8]  J R Fienup,et al.  Reconstruction of an object from the modulus of its Fourier transform. , 1978, Optics letters.

[9]  J. A. Hartigan,et al.  A k-means clustering algorithm , 1979 .

[10]  James R. Fienup,et al.  Iterative Method Applied To Image Reconstruction And To Computer-Generated Holograms , 1980 .

[11]  Michael A. Saunders,et al.  LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares , 1982, TOMS.

[12]  J R Fienup,et al.  Phase retrieval algorithms: a comparison. , 1982, Applied optics.

[13]  R. Fletcher.  A model algorithm for composite nondifferentiable optimization problems , 1982 .

[14]  Rainer Hettich,et al.  A Review of Numerical Methods for Semi-Infinite Optimization , 1983 .

[15]  James V. Burke,et al.  Descent methods for composite nondifferentiable optimization problems , 1985, Math. Program..

[16]  P. Rousseeuw.  Multivariate estimation with high breakdown point , 1985 .

[17]  Ya-Xiang Yuan,et al.  On the superlinear convergence of a trust region algorithm for nonsmooth optimization , 1985, Math. Program..

[18]  Rick P. Millane,et al.  Phase retrieval in crystallography and optics , 1990 .

[19]  Stephen J. Wright.  Convergence of an inexact algorithm for composite nonsmooth optimization , 1990 .

[20]  Michael W. Farn.  New iterative algorithm for the design of phase-only gratings , 1991, Optics & Photonics.

[21]  John N. Tsitsiklis,et al.  An Analysis of Stochastic Shortest Path Problems , 1991, Math. Oper. Res..

[22]  J. Kyparisis,et al.  Finite convergence of algorithms for nonlinear programs and variational inequalities , 1991 .

[23]  Robert W. Harrison,et al.  Phase problem in crystallography , 1993 .

[24]  M. Ferris,et al.  Weak sharp minima in mathematical programming , 1993 .

[25]  A. Szöke.  Holographic microscopy with a complicated reference : Holography II , 1997 .

[26]  J. Miao,et al.  Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens , 1999, Nature.

[27]  S. A. Werner,et al.  Imaging: Phase radiography with neutrons , 2000, Nature.

[28]  Jianqing Fan,et al.  Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties , 2001 .

[29]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[30]  James V. Burke,et al.  Optical Wavefront Reconstruction: Theory and Numerical Methods , 2002, SIAM Rev..

[31]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[32]  Adrian S. Lewis,et al.  A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization , 2005, SIAM J. Optim..

[33]  Yurii Nesterov,et al.  Smooth minimization of non-smooth functions , 2005, Math. Program..

[34]  Yurii Nesterov,et al.  Modified Gauss–Newton scheme with worst case guarantees for global performance , 2007, Optim. Methods Softw..

[35]  S. Sathiya Keerthi,et al.  Optimization Techniques for Semi-Supervised Support Vector Machines , 2008, J. Mach. Learn. Res..

[36]  Tom Goldstein,et al.  The Split Bregman Method for L1-Regularized Problems , 2009, SIAM J. Imaging Sci..

[37]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[38]  Katya Scheinberg,et al.  Introduction to derivative-free optimization , 2010, Math. Comput..

[39]  Junfeng Yang,et al.  Alternating Direction Algorithms for 1-Problems in Compressive Sensing , 2009, SIAM J. Sci. Comput..

[40]  Patrick L. Combettes,et al.  Proximal Splitting Methods in Signal Processing , 2009, Fixed-Point Algorithms for Inverse Problems in Science and Engineering.

[41]  Emmanuel J. Candès,et al.  NESTA: A Fast and Accurate First-Order Method for Sparse Recovery , 2009, SIAM J. Imaging Sci..

[42]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[43]  Nicholas I. M. Gould,et al.  On the Evaluation Complexity of Composite Function Minimization with Applications to Nonconvex Nonlinear Programming , 2011, SIAM J. Optim..

[44]  Yonina C. Eldar,et al.  Phase Retrieval: Stability and Recovery Guarantees , 2012, ArXiv.

[45]  Christophe Croux,et al.  Sparse least trimmed squares regression for analyzing high-dimensional large data sets , 2013, 1304.4773.

[46]  Bastian Goldlücke,et al.  Variational Analysis , 2014, Computer Vision, A Reference Guide.

[47]  Stephen P. Boyd,et al.  Proximal Algorithms , 2013, Found. Trends Optim..

[48]  Marc Teboulle,et al.  Proximal alternating linearized minimization for nonconvex and nonsmooth problems , 2013, Mathematical Programming.

[49]  Eric C. Chi,et al.  Splitting Methods for Convex Clustering , 2013, Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America.

[50]  Jane J. Ye,et al.  Smoothing augmented Lagrangian method for nonsmooth constrained optimization problems , 2015, J. Glob. Optim..

[51]  Yonina C. Eldar,et al.  Phase Retrieval via Matrix Completion , 2011, SIAM Rev..

[52]  Stephen J. Wright,et al.  A proximal method for composite minimization , 2008, Mathematical Programming.

[53]  Wotao Yin,et al.  Global Convergence of ADMM in Nonconvex Nonsmooth Optimization , 2015, Journal of Scientific Computing.

[54]  Aleksandr Y. Aravkin,et al.  Trimmed Statistical Estimation via Variance Reduction , 2020, Math. Oper. Res..