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This paper proposes efficient policy iteration and value iteration algorithms for the continuous-time linear quadratic regulator problem with unmeasurable states and unknown system dynamics, from the perspective of direct data-driven…

The Arnoldi-Tikhonov method is a well-established regularization technique for solving large-scale ill-posed linear inverse problems. This method leverages the Arnoldi decomposition to reduce computational complexity by projecting the…

In this contribution we present an accelerated optimization-based approach for combined state and parameter reduction of a parametrized linear control system which is then used as a surrogate model in a Bayesian inverse setting. Following…

Many systems are subject to periodic disturbances and exhibit repetitive behaviour. Model-based repetitive control employs knowledge of such periodicity to attenuate periodic disturbances and has seen a wide range of successful industrial…

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations…

We present iterative solvers to approximate the solution of numerical schemes for stochastic Stefan problems. After briefly talking about the convergence results, we tackle the question of efficient strategies for solving the nonlinear…

We propose and analyze an accelerated iterative dual diagonal descent algorithm for the solution of linear inverse problems with general regularization and data-fit functions. In particular, we develop an inertial approach of which we…

This survey is written in summer, 2016. The purpose of this survey is to briefly introduce nonlinear dimensionality reduction (NLDR) in data reduction. The first two NLDR were respectively published in Science in 2000 in which they solve…

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…

Generative Adversarial Networks (GANs) have been shown to be powerful and flexible priors when solving inverse problems. One challenge of using them is overcoming representation error, the fundamental limitation of the network in…

In this work, we propose a data-driven scheme to initialize the parameters of a deep neural network. This is in contrast to traditional approaches which randomly initialize parameters by sampling from transformed standard distributions.…

Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…

For the solution of discrete ill-posed problems, in this paper a novel preconditioned iterative method based on the Arnoldi algorithm for matrix functions is presented. The method is also extended to work in connection with Tikhonov…

Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…

Many challenging image processing tasks can be described by an ill-posed linear inverse problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all lie in this framework. Traditional inverse problem solvers…

This paper focuses on the stabilization and regulation of linear systems affected by quantization in state-transition data and actuated input. The observed data are composed of tuples of current state, input, and the next state's interval…

Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how…

Learning, say through direct policy updates, often requires assumptions such as knowing a priori that the initial policy (gain) is stabilizing, or persistently exciting (PE) input-output data, is available. In this paper, we examine online…