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

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Abstract
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.
Funding Information
  • National Science Foundation (CIF 1632599, CIF 1564044, CAREER Award 1555850)
  • Office of Naval Research (N00014-16-1-2244)
  • MIUR project PLATINO (PON01_01007)

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