Parallel and Distributed Methods for Constrained Nonconvex Optimization—Part I: Theory

In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints, and also consider extensions to some structured, nonsmooth problems. The algorithm solves a sequence of (separable) strongly convex problems...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 65; no. 8; pp. 1929 - 1944
Main Authors: Scutari, Gesualdo, Facchinei, Francisco, Lampariello, Lorenzo
Format: Journal Article
Language:English
Published: IEEE 15.04.2017
Subjects:
Ad hoc networks
Approximation algorithms
Convergence
Distributed algorithms
Linear programming
nonconvex optimization
Optimization
Signal processing algorithms
successive convex approximation
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints, and also consider extensions to some structured, nonsmooth problems. The algorithm solves a sequence of (separable) strongly convex problems and maintains feasibility at each iteration. Convergence to a stationary solution of the original nonconvex optimization is established. Our framework is very general and flexible and unifies several existing successive convex approximation (SCA)-based algorithms. More importantly, and differently from current SCA approaches, it naturally leads to distributed and parallelizable implementations for a large class of nonconvex problems. This Part I is devoted to the description of the framework in its generality. In Part II, we customize our general methods to several (multiagent) optimization problems in communications, networking, and machine learning; the result is a new class of centralized and distributed algorithms that compare favorably to existing ad-hoc (centralized) schemes.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2016.2637317