Abstract
Stochastic optimal control problems are typically of rather large scale involving millions of decision variables, but possess a certain structure which can be exploited by first-order methods such as forward-backward splitting and the alternating direction method of multipliers (ADMM). In this paper, we use the forward-backward envelope, a real-valued continuously differentiable penalty function, to recast the dual of the original nonsmooth problem as an unconstrained problem which we solve via the limited-memory BFGS algorithm. We show that the proposed method leads to a significant improvement of the convergence rate without increasing much the computational cost per iteration.
Highlights
1.1 Motivation and BackgroundScenario-based stochastic model predictive control is becoming increasingly popular in control applications for its ability to deliver control actions with foresight under uncertainty and has been used for the control of power dispatch (Hans et al, 2015; Patrinos et al, 2011), HVAC of buildings (Zhang et al, 2013), macroeconomic systems (Patrinos et al, 2014), supply chains (Schildbach and Morari, 2016) and many another
In this paper we show that the application of the limited-memory BFGS (L-BFGS) method to the forward-backward envelope (FBE) leads to a noticeable improvement of the convergence speed without a significant increase in the computational cost per iteration
We previously showed that stochastic optimal control problems possess a certain structure which can be exploited for their efficient numerical solution using an accelerated proximal gradient (APG) algorithm (Sampathirao et al, 2015)
Summary
Scenario-based stochastic model predictive control is becoming increasingly popular in control applications for its ability to deliver control actions with foresight under uncertainty and has been used for the control of power dispatch (Hans et al, 2015; Patrinos et al, 2011), HVAC of buildings (Zhang et al, 2013), macroeconomic systems (Patrinos et al, 2014), supply chains (Schildbach and Morari, 2016) and many another. The limited-memory BFGS (L-BFGS) method has been successfully used for the numerical solution of unconstrained problems (Liu and Nocedal, 1989) and recently for huge-scale problems (Chen et al, 2014) It implicitly updates a diagonal approximation of the Hessian using a computationally cheap algorithm known as the two-loop recursion (Nocedal and Wright, 2006). Despite its popularity it comes with two limitations which have hindered its use for the solution of optimal control problems. In this paper we show that the application of the L-BFGS method to the FBE leads to a noticeable improvement of the convergence speed without a significant increase in the computational cost per iteration
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
