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Prodotti recenti

Asymmetric forward–backward–adjoint splitting for solving monotone inclusions involving three operators

In this work we propose a new splitting technique, namely Asymmetric Forward–Backward–Adjoint splitting, for solving monotone inclusions involving three terms, a maximally monotone, a cocoercive and a bounded linear operator. Our scheme can not be recovered from existing operator splitting methods, while classical methods like Douglas–Rachford and Forward–Backward splitting are special cases of the new algorithm. Asymmetric preconditioning is the main feature of Asymmetric Forward–Backward–Ad...

Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradient

Backtracking linesearch is the de facto approach for minimizing continuously differentiable functions with locally Lipschitz gradient. In recent years, it has been shown that in the convex setting it is possible to avoid linesearch altogether, and to allow the stepsize to adapt based on a local smoothness estimate without any backtracks or evaluations of the function value. In this work we propose an adaptive proximal gradient method, adaPGM, that uses novel estimates of the local smoothness ...

A new randomized block-coordinate primal-dual proximal algorithm for distributed optimization

This paper proposes Triangularly Preconditioned Primal- Dual algorithm, a new primal-dual algorithm for minimizing the sum of a Lipschitz-differentiable convex function and two possibly nonsmooth convex functions, one of which is composed with a linear mapping. We devise a randomized block-coordinate ( BC) version of the algorithm which converges under the same stepsize conditions as the full algorithm. It is shown that both the original as well as the BC scheme feature linear convergence rat...

New primal-dual proximal algorithm for distributed optimization

We consider a network of agents, each with its own private cost consisting of the sum of two possibly nonsmooth convex functions, one of which is composed with a linear operator. At every iteration each agent performs local calculations and can only communicate with its neighbors. The goal is to minimize the aggregate of the private cost functions and reach a consensus over a graph. We propose a primal-dual algorithm based on Asymmetric Forward-Backward-Adjoint (AFBA), a new operator splittin...

Escaping limit cycles: Global convergence for constrained nonconvex-nonconcave minimax problems

This paper introduces a new extragradient-type algorithm for a class of nonconvex-nonconcave minimax problems. It is well-known that finding a local solution for general minimax problems is computationally intractable. This observation has recently motivated the study of structures sufficient for convergence of first order methods in the more general setting of variational inequalities when the so-called weak Minty variational inequality (MVI) holds. This problem class captures non-trivial st...

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