Proximity for sums of composite functions

By Patrick L. Combettes, D. Dung, Bang Công Vu. 2010

70 citations recorded by the source corpus.

We propose an algorithm for computing the proximity operator of a sum of composite convex functions in Hilbert spaces and investigate its asymptotic behavior. Applications to best approximation and image recovery are described.

Subfields: Computational Mechanics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5ee54cf1a9b127a4b87077f0ecd112351c318b88

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In Computational Mechanics

In Mathematical Physics

In Numerical Analysis

Citations in the corpus

A splitting algorithm for dual monotone inclusions involving cocoercive operators (2011, background): “pplied mathematics, e.g., evolution inclusions [2], partial diﬀerential equations [1, 20, 23], mechanics [21], variational inequalities [6, 19], Nash equilibria [8], and various optimization problems [7, 9, 10, 14, 15, 17, 25, 29]. In such formulations, cocoercivity often plays a central role; see f”
A Primal–Dual Splitting Method for Convex Optimization Involving Lipschitzian, Proximable and Linear Composite Terms (2012, methodology): “The most classical operator splitting methods to minimize the sum of two convex functions are the forward–backward method, proposed in [2] and further developed in [3, 4, 7, 25–28], and the Douglas–Rachford method [3, 6, 7, 22].”
Variable metric forward–backward splitting with applications to monotone inclusions in duality (2012, background): “It also extends the framework of [14], where f1⁄4 0 and (8i2 {1, .”