An augmented Lagrangian interior-point approach for large-scale NLP problems on graphics processing units

Cao, Yankai; Seth, Arpan; Laird, Carl D.

doi:10.1016/j.compchemeng.2015.10.010

Cited by 26 publications

(21 citation statements)

References 29 publications

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“…Moreover, in connection with paper E, an augmented Lagrangian interior-point approach is presented in Cao et al (2016), where the linear KKT system is solved using a preconditioned conjugate gradient method, which is implemented efficiently on a Graphics Processing Unit (GPU) in parallel. For sufficiently sparse problems, one possible future work is to distribute the computations of the preconditioned conjugate gradient used for solving the KKT system, over the clique tree of the problem such that parallelism can be exploited.…”

Section: Concluding Remarks and Future Workmentioning

confidence: 99%

Distributed Optimization for Control and Estimation

Ahmadi

2022

Linköping Studies in Science and Technology. Dissertations

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Adopting centralized optimization approaches in order to solve optimization problem arising from analyzing large-scale systems, requires a powerful computational unit. Such units, however, do not always exist. In addition, it is not always possible to form the optimization problem in a centralized manner due to structural constraints or privacy requirements. A possible solution in these cases is to use distributed optimization approaches. Many large-scale systems have inherent structures which can be exploited to develop scalable optimization approaches. In this thesis, chordal graph properties are used in order to design tailored distributed optimization approaches for applications in control and estimation, and especially for model predictive control and localization problems. The first contribution concerns a distributed primal-dual interior-point algorithm for which it is investigated how parallelism can be exploited. In particular, it is shown how the computations of the algorithm can be distributed on different processors so that they can be run in parallel. As a result, the algorithm execution time is accelerated compared to the case where the algorithm is run on a single processor. Simulation studies on linear model predictive control and robust model predictive control confirm the efficiency of the framework. The second contribution is to devise a tailored distributed algorithm for nonlinear least squares with application to a sensor network location problem. It relies on the Levenberg-Marquardt algorithm, in which the computations are distributed using message passing over the computational graph of the problem, which is obtained from what is known as the clique tree of the problem. The results indicate that the algorithm provides not only a good localization accuracy, but also it requires fewer iterations and communications between computational agents in order to converge compared to known first-order methods. The third contribution is a study of extending the message passing idea in order to design tailored distributed algorithm for general non-convex problems. The framework relies on an augmented Lagrangian algorithm in which a primal-dual interior-point method is used for the inner iteration. Application of the framework for general model predictive control of systems with several interconnected sub-systems is extensively investigated. The performance of the framework is then compared with distributed methods based on the alternating direction method of multipliers, where the superiority of the framework is illustrated. v I would like to start by expressing my deepest respect and gratitude to my supervisor, Anders Hansson, for the opportunity you gave me to pursue my PhD, for your excellent guidance, continuous support, and encouragement throughout this journey. I am sincerely grateful for the positive impact you had in this chapter of my life, for your inspiring ideas, positive attitude, resourcefulness, and of course your patience! Thank you Anders! I would also like to thank Anders Helmersson an...

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Section: Concluding Remarks and Future Workmentioning

confidence: 99%

Distributed Optimization for Control and Estimation

Ahmadi

2022

Linköping Studies in Science and Technology. Dissertations

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“…Other approaches to improve online applicability of optimizationbased methods are based on making the computational process faster. This could be achieved by improving the computational performance of the underlying methods, e.g., obtaining a solution of the linear system of equations arising at each step of many iterative optimization solvers faster [59], or by not fully solving the optimization problem at each step when a sequence of slightly changing problems is computed. Solutions using sequentially quadratic methods could in some cases be of sufficient quality for feedback control after just one iteration [55].…”

Section: Computational Aspects Of Optimizationmentioning

confidence: 99%

Autonomous Avoidance Maneuvers for Vehicles using Optimization

Anistratov

2021

Linköping Studies in Science and Technology. Dissertations

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“…Other approaches to improve online applicability of optimization-based methods are based on making the computational process faster. This could be achieved by improving the computational performance of the underlying methods, e.g., obtaining a solution of the linear system of equations arising at each step of many iterative optimization solvers faster (Cao et al, 2016), or by not fully solving the optimization problem at each step when a sequence of slightly changing problems are computed. For interior-point methods, this could be achieved by early termination based on a small number of maximum iterations, or not updating the barrier penalty parameter, which also allows taking advantage of warm starting the solver (Wang and Boyd, 2010).…”

Section: Computational Aspects Of Optimizationmentioning

confidence: 99%