Consensus Accelerated Proximal Reweighted Iteration for a Class of Nonconvex Minimizations (Capri)

PROJECT TITLE :

Capri: Consensus Accelerated Proximal Reweighted Iteration for A Class of Nonconvex Minimizations

ABSTRACT:

In this paper, we investigate a category of nonconvex regularized optimization problems, the likes of which are common in the fields of Machine Learning and data processing. The structure of the problems necessitated the development of the iteratively reweighted algorithm, which was then utilized in the process of consensus optimization. We propose in this paper that an acceleration of this scheme can be achieved by including an inertial term in each iteration of the calculation. The proposed algorithms inherit the benefits of traditional decentralized algorithms, such as the fact that they are able to be implemented over a connected network in which the agents communicate with their neighbors and carry out local computations. We also use a technique called diminishing stepsizes for the iteratively reweighted algorithm, and we take the acceleration of that algorithm into consideration. In certain circumstances, our algorithms can be reduced to already established decentralized systems, in addition to indicating newly developed ones. Mathematically speaking, we demonstrate the convergence of both algorithms by making a number of assumptions regarding the objective functions. The Kurdyka-Ojasiewicz property allows for the derivation of convergence rates in the case of constant step size. The effectiveness of the algorithms is demonstrated through the use of numerical results.

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