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Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables.
The differentiation of pseudo-inverses and nonlinear least squares which variables separate
G.H. Golub and V. Pereyra · 1973
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Algorithms for separable nonlinear least squares problems
A. Ruhe and P.A. Wedin · 1980
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Least Median of Squares Regression
P. J Rousseeuw · 1984
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Some interlacing properties of the Schur complement of a Hermitian matrix
Ronald L. Smith · 1992
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Variational Analysis
R.T. Rockafellar and R.J.B. Wets · 1998
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Separable nonlinear least squares: the variable projection method and its applications
G.H. Golub and V. Pereyra · 2003
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Separable least squares, variable projection, and the Gauss-Newton algorithm
M.R. Osborne · 2007
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Algorithmic differentiation of implicit functions and optimal values
B.M. Bell and J.V. Burke · 2008
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Convergence rates of inexact proximal-gradient methods for convex optimization
Mark Schmidt, Nicolas L Roux, and Francis R Bach · 2011
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Estimating nuisance parameters in inverse problems
Aleksandr Y. Aravkin and Tristan van Leeuwen · 2012
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Constrained variable projection method for blind deconvolution
Anastasia Cornelio, E. Loli Piccolomini, and J. G. Nagy · 2012
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Exponential Data Fitting and its Applications
V. Pereyra and G. Scherer, editors · 2012
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A generalization of variable elimination for separable inverse problems beyond least squares
Paul Shearer and Anna C Gilbert · 2013
Projection onto the capped simplex
Weiran Wang and Canyi Lu · 2015
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A smart stochastic algorithm for nonconvex optimization with applications to robust machine learning
Aleksandr Aravkin and Damek Davis · 2016
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First-Order Methods in Optimization
Amir Beck · 2017
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Automatic alignment for three-dimensional tomographic reconstruction
Tristan van Leeuwen, Simon Maretzke, and K Joost Batenburg · 2018
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A general family of trimmed estimators for robust high-dimensional data analysis
Eunho Yang, Aurélie C Lozano, Aleksandr Aravkin, et al · 2018
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First-order methods of smooth convex optimization with inexact oracle
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