Constrained policy optimization for stochastic optimal control under nonstationary uncertainties via Markov embeddability and finite approximation.
Graph-Based Modeling and Decomposition of Energy Infrastructures
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abstract
Nonlinear optimization problems are found at the heart of real-time operations of critical infrastructures. These problems are computationally challenging because they embed complex physical models that exhibit space-time dynamics. We propose modeling these problems as graph-structured optimization problems, and illustrate how their structure can be exploited at the modeling level (for parallelizing function/derivative computations) and at the solver level (for parallelizing linear algebra operations). Specifically, we present a restricted additive Schwarz scheme that enables flexible decomposition of complex graph structures within an interior-point algorithm. The proposed approach is implemented as a general-purpose nonlinear programming solver that we call MadNLP.jl; this Julia-based solver is interfaced to the graph-based modeling package Plasmo.jl. The efficiency of this framework is demonstrated via problems arising in transient gas network optimization and multi-period AC optimal power flow. We show that our framework accelerates the solution (compared to off-the-shelf tools) by over 300%; specifically, solution times are reduced from 72.36 sec to 23.84 sec for the gas problem and from 515.81 sec to 149.45 sec for the power flow problem.
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UNVERDICTED 3representative citing papers
A novel feasible-path method solves optimal power flow in reduced space by directly enforcing power flow equations and softly penalizing operational constraints via Augmented Lagrangian, with GPU acceleration for the reduced Hessian.
Overlapping Schwarz decomposition for nonlinear OCPs achieves local linear convergence with rate improving exponentially with overlap size, based on exponential decay of sensitivity for primal and dual solutions.
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Constrained Policy Optimization for Stochastic Optimal Control under Nonstationary Uncertainties
Constrained policy optimization for stochastic optimal control under nonstationary uncertainties via Markov embeddability and finite approximation.
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A Feasible Reduced Space Method for Real-Time Optimal Power Flow
A novel feasible-path method solves optimal power flow in reduced space by directly enforcing power flow equations and softly penalizing operational constraints via Augmented Lagrangian, with GPU acceleration for the reduced Hessian.
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On the Convergence of Overlapping Schwarz Decomposition for Nonlinear Optimal Control
Overlapping Schwarz decomposition for nonlinear OCPs achieves local linear convergence with rate improving exponentially with overlap size, based on exponential decay of sensitivity for primal and dual solutions.