Overview
ABSTRACT
The proximal gradient method is a splitting algorithm for the minimization of the sum of two convex functions, one of which is smooth. It has applications in areas such as mechanics, inverse problems, machine learning, image reconstruction, variational inequalities, statistics, operations research, and optimal transportation. Its formalism encompasses a wide variety of numerical methods in optimization such as gradient descent, projected gradient, iterative thresholding, alternating projections, the constrained Landweber method, as well as various algorithms in statistics and sparse data analysis. This paper aims at providing an account of the main properties of the proximal gradient method and to discuss some of its applications.
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Patrick L. COMBETTES: North Carolina State University - Department of Mathematics - Raleigh, NC 27695, United States
INTRODUCTION
Notations. , and are Euclidean spaces, i.e. real Hilbertian spaces of finite dimension. Note their scalar product and the associated norm. A function is clean if . The class of lower, convex and proper semicontinuous functions of in is noted . Finally, ...
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KEYWORDS
splitting algorithm | convex function | numerical methods in optimization | gradient descent
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The proximal gradient method
Mathematical framework
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