Advanced Techniques in Optimization for Machine Learning and Imaging, Benfenati A., Porta F., 2024

Advanced Techniques in Optimization for Machine Learning and Imaging, Benfenati A., Porta F., 2024.
     
    In recent years, non-linear optimization has had a crucial role in the development of modern techniques at the interface of machine learning and imaging. The present book is a collection of recent contributions in the field of optimization, either revisiting consolidated ideas to provide formal theoretical guarantees or providing comparative numerical studies for challenging inverse problems in imaging. The work of these papers originated in the INdAM Workshop “Advanced Techniques in Optimization for Machine learning and Imaging” held in Roma, Italy, on June 20–24, 2022.




Non-convex Problems.
To test the performance of the inexact proximal Gauss–Newton method on non-convex problems, we considered modified versions of nonlinear non-convex opti-mization problems from [ 7]. In detail, as done in [ 11] we took 3 unconstrained opti-mization problems (Rosenbrock, Osborne1, and Kowalik) and equipped them with bound constraints, thus obtaining problems of the form (script upper PP) whereupper J J models the bound constraints (see [ 11, Section 8] for further details).

Again we considered inexact proximal Gauss–Newton approaches by setting a prefixed number of inner iterations of the solver for the minimization subproblems. In this case they are bound-constrained least squares problems which we solved by a proximal gradient method. In detail we considered a maximum number of inner solver iterationsupper M M equal to100 100,50 50,10 10, and55 and compared the four resulting algo-rithms (named respectively GN_100, GN_50, GN_10, and GN_5) with the proximal gradient (indicated as PG) method applied directly to the original problem. It is worth mentioning that for the inner problems in the inexact Gauss–Newton imple-mentations we used a fixed steplength related to the subproblem Lipschitz constant.

CONTENTS.
STEMPO—Dynamic X-Ray Tomography Phantom.
On a Fixed-Point Continuation Method for a Convex Optimization Problem.
Majoration-Minimization for Sparse SVMs.
Bilevel Learning of Regularization Models and Their Discretization for Image Deblurring and Super-Resolution.
Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithms.
On the Inexact Proximal Gauss–Newton Methods for Regularized Nonlinear Least Squares Problems.



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