Primal and Dual Prediction-Correction Methods for Time-Varying Convex Optimization

Bastianello, Nicola; Simonetto, Andrea; Carli, Ruggero

doi:10.48550/arxiv.2004.11709

Cited by 5 publications

(25 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then an approximate solution of the predicted problem can be used to warm-start the solver 1 when applied to the actual problem. As proved in [11], this approach allows to reduce the tracking error.…”

Section: Predictionmentioning

confidence: 92%

“…In this section we review the approach to time-varying optimization that informed the design of the tvopt framework. We refer the interested reader to the theoretical framework developed in [11] and the surveys [3], [4] for more details.…”

Section: Time-varying Optimizationmentioning

confidence: 99%

“…As proposed in [6], [10] and further extended in [11], the knowledge of past sampled problems can be exploited to improve the tracking of the optimal trajectory. Indeed, the information collected up to time t k can be used to shape a prediction of the (as yet unobserved) problem at time t k+1 .…”

Section: Predictionmentioning

confidence: 99%

“…To conclude this section, we detail the steps of a prediction-correction method for solving (3), see Figure 1, and refer to [11] for further details.…”

Section: Predictionmentioning

confidence: 99%

“…[5], [6], and in decentralized scenarios [7]- [9]. An interesting approach to developing online algorithms is that of prediction-correction, proposed in [6], [10] and extended in [11]. The main idea is to exploit past information on the problem to improve the solution accuracy of the algorithm.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

tvopt: A Python Framework for Time-Varying Optimization

Bastianello¹

2020

Preprint

Self Cite

View full text Add to dashboard Cite

This paper introduces tvopt, a Python framework for prototyping and benchmarking time-varying (or online) optimization algorithms. The paper first describes the theoretical approach that informed the development of tvopt. Then it discusses the different components of the framework and their use for modeling and solving time-varying optimization problems. In particular, tvopt provides functionalities for defining both centralized and distributed online problems, and a collection of built-in algorithms to solve them, for example gradient-based methods, ADMM and other splitting methods. Moreover, the framework implements prediction strategies to improve the accuracy of the online solvers. The paper then proposes some numerical results on a benchmark problem and discusses their implementation using tvopt. The code for tvopt is available at [1].

show abstract

Section: Predictionmentioning

confidence: 92%

Section: Time-varying Optimizationmentioning

confidence: 99%

Section: Predictionmentioning

confidence: 99%

“…To conclude this section, we detail the steps of a prediction-correction method for solving (3), see Figure 1, and refer to [11] for further details.…”

Section: Predictionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

tvopt: A Python Framework for Time-Varying Optimization

Bastianello¹

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Prediction-Correction Splittings for Nonsmooth Time-Varying Optimization

Bastianello

Simonetto

Carli

2019

2019 18th European Control Conference (ECC)

Self Cite

View full text Add to dashboard Cite

We address the solution of time-varying optimization problems characterized by the sum of a time-varying strongly convex function and a time-invariant nonsmooth convex function. We design an online algorithmic framework based on prediction-correction, which employs splitting methods to solve the sampled instances of the time-varying problem. We describe the prediction-correction scheme and two splitting methods, the forward-backward and the Douglas-Rachford. Then by using a result for generalized equations, we prove convergence of the generated sequence of approximate optimizers to a neighborhood of the optimal solution trajectory. Simulation results for a leader following formation in robotics assess the performance of the proposed algorithm.

show abstract

Optimization Algorithms as Robust Feedback Controllers

Hauswirth¹,

Bolognani²,

Hug³

et al. 2021

Preprint

View full text Add to dashboard Cite

Mathematical optimization is one of the cornerstones of modern engineering research and practice. Yet, throughout all application domains, mathematical optimization is, for the most part, considered to be a numerical discipline. Optimization problems are formulated to be solved numerically with specific algorithms running on microprocessors. An emerging alternative is to view optimization algorithms as dynamical systems. While this new perspective is insightful in itself, liberating optimization methods from specific numerical and algorithmic aspects opens up new possibilities to endow complex real-world systems with sophisticated self-optimizing behavior. Towards this goal, it is necessary to understand how numerical optimization algorithms can be converted into feedback controllers to enable robust "closed-loop optimization". In this article, we review several research streams that have been pursued in this direction, including extremum seeking and pertinent methods from model predictive and process control. However, our primary focus lies on recent methods under the name of "feedback-based optimization". This research stream studies control designs that directly implement optimization algorithms in closed loop with physical systems. Such ideas are finding widespread application in the design and retrofit of control protocols for communication networks and electricity grids. In addition to an overview over continuous-time dynamical systems for optimization, our particular emphasis in this survey lies on closed-loop stability as well as the enforcement of physical and operational constraints in closed-loop implementations. We further illustrate these methods in the context of classical problems, namely congestion control in communication networks and optimal frequency control in electricity grids, and we highlight one potential future application in the form of autonomous reserve dispatch in power systems.

show abstract

Primal and Dual Prediction-Correction Methods for Time-Varying Convex Optimization

Cited by 5 publications

References 0 publications

tvopt: A Python Framework for Time-Varying Optimization

tvopt: A Python Framework for Time-Varying Optimization

Prediction-Correction Splittings for Nonsmooth Time-Varying Optimization

Optimization Algorithms as Robust Feedback Controllers

Contact Info

Product

Resources

About