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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| Vydané v: | IEEE transactions on signal processing Ročník 65; číslo 8; s. 1929 - 1944 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
IEEE
15.04.2017
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| ISSN: | 1053-587X, 1941-0476 |
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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. |
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| AbstractList | 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. |
| Author | Scutari, Gesualdo Facchinei, Francisco Lampariello, Lorenzo |
| Author_xml | – sequence: 1 givenname: Gesualdo surname: Scutari fullname: Scutari, Gesualdo email: gscutari@purdue.edu organization: School of Industrial Engineering and the Cyber Center (Discovery Park), Purdue University, West-Lafayette, IN, USA – sequence: 2 givenname: Francisco surname: Facchinei fullname: Facchinei, Francisco email: facchinei@diag.uniroma1.it organization: Department of Computer, Control, and Management Engineering, University of Rome "La Sapienza", Rome, Italy – sequence: 3 givenname: Lorenzo surname: Lampariello fullname: Lampariello, Lorenzo email: lorenzo.lampariello@uniroma3.it organization: Department of Business Studies, University of RomaTre, Roma, Italy |
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| SubjectTerms | Ad hoc networks Approximation algorithms Convergence Distributed algorithms Linear programming nonconvex optimization Optimization Signal processing algorithms successive convex approximation |
| Title | Parallel and Distributed Methods for Constrained Nonconvex Optimization—Part I: Theory |
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