Dual Prediction-Correction Methods for Linearly Constrained Time-Varying Convex Programs

Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track the optimizer trajectory of the continuously-varying convex...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 64; no. 8; pp. 3355 - 3361
Main Author: Simonetto, Andrea
Format: Journal Article
Language:English
Published: New York IEEE 01.08.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Asymptotic methods
Asymptotic properties
Computational geometry
Convergence
Convex analysis
Convex functions
Convexity
Cost function
Dual ascent
Error correction
Iterative algorithms
Iterative methods
Machine learning
parametric programming
Prediction algorithms
prediction–correction methods
Signal processing
Signal processing algorithms
time-varying convex optimization
Tracking errors
Trajectory
Trajectory optimization
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track the optimizer trajectory of the continuously-varying convex optimization program. Recently, a novel prediction-correction methodology has been put forward to set up iterative algorithms that sample the continuously-varying optimization program at discrete time steps and perform a limited amount of computations to correct their approximate optimizer with the new sampled problem and predict how the optimizer will change at the next time step. Prediction-correction algorithms have been shown to outperform more classical strategies, i.e., correction-only methods. Typically, prediction-correction methods have asymptotical tracking errors of the order of <inline-formula><tex-math notation="LaTeX">h^2</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">h</tex-math></inline-formula> is the sampling period, whereas classical strategies have order of <inline-formula><tex-math notation="LaTeX">h</tex-math></inline-formula>. Up to now, prediction-correction algorithms have been developed in the primal space, both for unconstrained and simply constrained convex programs. In this paper, we show how to tackle linearly constrained continuously-varying problem by prediction-correction in the dual space and we prove similar asymptotical error bounds as their primal versions.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2018.2877682