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The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
In this paper, we propose a combined Magnitude Saturated Adaptive Control (MSAC)-Model Predictive Control (MPC) approach to linear quadratic tracking optimal control problems with parametric uncertainties and input saturation. The proposed…
We propose a solution strategy for linear systems arising in interior method optimization, which is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for solving these…
Ising computing provides a new computing paradigm for many hard combinatorial optimization problems. Ising computing essentially tries to solve the quadratic unconstrained binary optimization problem, which is also described by the Ising…
Linear Programming (LP) is a foundational optimization technique with widespread applications in finance, energy trading, and supply chain logistics. However, traditional Central Processing Unit (CPU)-based LP solvers often struggle to meet…
Parallel computing can offer an enormous advantage regarding the performance for very large applications in almost any field: scientific computing, computer vision, databases, data mining, and economics. GPUs are high performance many-core…
Security-Constrained Unit Commitment is a fundamental optimization problem in power systems operations. The primary computational bottleneck arises from the need to solve large-scale Linear Programming (LP) relaxations within…
In this paper we propose a constrained guaranteed cost robust model predictive controller (GCMPC) for uncertain discrete time systems. This controller was developed based on a quadratic cost functional and guarantee robustness with respect…
Graphics Processing Units (GPUs) have become an integral part of High-Performance Computing to achieve an Exascale performance. The main goal of application developers of GPU is to tune their code extensively to obtain optimal performance,…
Particle swarm optimization is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The approach of particle swarms is an example for…
Model predictive control (MPC) is an optimal control technique which involves solving a sequence of constrained optimization problems across a given time horizon. In this paper, we introduce a category theoretic framework for constructing…
In this paper, we further develop a family of parallel time integrators known as Revisionist Integral Deferred Correction methods (RIDC) to allow for the semi-implicit solution of time dependent PDEs. Additionally, we show that our…
Model predictive control (MPC) is a powerful control method that handles dynamical systems with constraints. However, solving MPC iteratively in real time, i.e., implicit MPC, remains a computational challenge. To address this, common…
Multi-party computation (MPC) is promising for designing privacy-preserving machine learning algorithms at edge networks. An emerging approach is coded-MPC (CMPC), which advocates the use of coded computation to improve the performance of…
We consider Monte Carlo simulations of classical spin models of statistical mechanics using the massively parallel architecture provided by graphics processing units (GPUs). We discuss simulations of models with discrete and continuous…
Many geometry processing techniques require the solution of partial differential equations (PDEs) on manifolds embedded in $\mathbb{R}^2$ or $\mathbb{R}^3$, such as curves or surfaces. Such manifold PDEs often involve boundary conditions…
Modern graphics processing units (GPUs) provide impressive computing resources, which can be accessed conveniently through the CUDA programming interface. We describe how GPUs can be used to considerably speed up molecular dynamics (MD)…
In this work, we propose an output-feedback tube-based model predictive control (MPC) scheme for linear systems under dynamic uncertainties that are described via integral quadratic constraints (IQC). By leveraging IQCs, a large class of…
Quadratic cone programs are rapidly becoming the standard canonical form for convex optimization problems. In this paper we address the question of differentiating the solution map for such problems, generalizing previous work for linear…