We propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems. Converge...
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ISBN:
(纸本)9781479928934
We propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems. Convergence to a stationary solution of the original nonconvex optimization is established. Our framework is very general and flexible;it unifies several existing Successive Convex Approximation (SCA)-based algorithms such as (proximal) gradient or Newton type methods, block coordinate (parallel) descent schemes, difference of convex functions methods, and improves on their convergence properties. More importantly, and differently from current SCA schemes, it naturally leads to distributed and parallelizable schemes for a large class of nonconvex problems. The new method is applied to the solution of a new rate profile optimization problem over Interference Broadcast Channels (IBCs);numerical results show that it outperforms existing ad-hoc algorithms.
We propose a decomposition framework for the distributedoptimization of general noncoiwex stun-utility functions arising in the design of wireless multi-user interfering systems. Our main contributions are: i) the de...
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ISBN:
(纸本)9781479903566
We propose a decomposition framework for the distributedoptimization of general noncoiwex stun-utility functions arising in the design of wireless multi-user interfering systems. Our main contributions are: i) the development of the first provably convergent Jacobi bestresponse algorithm, where all users simultaneously solve a suitably convexified version of the original sum-utility optimization problem;ii) the derivation of a general dynamic pricing mechanism that provides a unified view of existing pricing schemes that are based, instead, on heuristics;and iii) a framework that can be easily particularized to well-known applications, giving rise to practical algorithms that outperform all existing ad-hoc methods proposed for very specific problems. Our framework contains as special cases wellknown gradient algorithms for nonconvex sum-utility problems, and many block-coordinate descents schemes for convex functions.
We propose a decomposition framework for the distributedoptimization of general nonconvex sum-utility functions arising in the design of wireless multi-user interfering systems. Our main contributions are: i) the dev...
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ISBN:
(纸本)9781479903573
We propose a decomposition framework for the distributedoptimization of general nonconvex sum-utility functions arising in the design of wireless multi-user interfering systems. Our main contributions are: i) the development of the first provably convergent Jacobi best-response algorithm, where all users simultaneously solve a suitably convexified version of the original sum-utility optimization problem;ii) the derivation of a general dynamic pricing mechanism that provides a unified view of existing pricing schemes that are based, instead, on heuristics;and iii) a framework that can be easily particularized to well-known applications, giving rise to practical algorithms that outperform all existing ad-hoc methods proposed for very specific problems. Our framework contains as special cases well-known gradient algorithms for nonconvex sum-utility problems, and many block-coordinate descents schemes for convex functions.
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