variable projection – Optimization Online

Constrained Variable Projection for Structured Problems

Published: 2026/06/24

Francesco Rinaldi

Bilevel Optimization, Nonlinear Optimization, Optimization in Data Science machine learning, numerical optimization, variable projection

Variable projection is a classical technique for separable nonlinear least-squares problems, in which variables that enter linearly are eliminated exactly, yielding a reduced nonlinear problem. By expressing this framework as a particular instance of a broader class of bilevel optimization problems, we develop a constrained variable-projection framework for data-science models, where the remaining variables are … Read more

NUMERICAL OPTIMIZATION METHODS FOR BLIND DECONVOLUTION

Published: 2012/02/12

Constrained Nonlinear Optimization, Nonlinear Systems and Least-Squares blind deconvolution, implicit filtering, nonlinear least squares, tikhonov regularization, variable projection

This paper describes a nonlinear least squares framework to solve a separable nonlinear ill-posed inverse problems that arises in blind deconvolution. It is shown that with proper constraints and well chosen regularization parameters, it is possible to obtain an objective function that is fairly well behaved and the nonlinear minimization problem can be effectively solved … Read more