Anzeige
Erschienen in:
2011 | OriginalPaper | Buchkapitel
Graph-Matrix Calculus for Computational Convex Analysis
verfasst von : Bryan Gardiner, Yves Lucet
Erschienen in: Fixed-Point Algorithms for Inverse Problems in Science and Engineering
Verlag: Springer New York
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
We introduce a new family of algorithms for computing fundamental operators arising from convex analysis. The new algorithms rely on the fact that the graph of the subdifferential of most convex operators depends linearly on the graph of the subdifferential of the function. By storing the subdifferential information, the computation of the conjugate is reduced to a matrix multiplication. We explain how other operators can be computed similarly, and present numerical experiments that compare graph-matrix calculus algorithms with piecewise-linear quadratic algorithms from computational convex analysis (CCA), and with a bundle method using warmstarting. Our results show that the new algorithms are an order of magnitude faster. They also add subdifferential calculus to our numerical library, and are very simple to implement.