Related papers: The Mermin fixed point
We survey the main numerical techniques for finite-dimensional nonlinear optimal control. The chapter is written as a guide to practitioners who wish to get rapidly acquainted with the main numerical methods used to efficiently solve an…
We propose a methodology, based on machine learning and optimization, for selecting a solver configuration for a given instance. First, we employ a set of solved instances and configurations in order to learn a performance function of the…
In this work, we state a general conjecture on the solvability of optimization problems via algorithms with linear convergence guarantees. We make a first step towards examining its correctness by fully characterizing the problems that are…
Classical control of cyber-physical systems used to rely on basic linear controllers. These controllers provided a safe and robust behavior but lack the ability to perform more complex controls such as aggressive maneuvering or performing…
The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. We…
In model predictive control (MPC) an optimization problem has to be solved at each time step, which in real-time applications makes it important to solve these optimization problems efficiently and to have good upper bounds on worst-case…
The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
Generative models based on flow matching have attracted significant attention for their simplicity and superior performance in high-resolution image synthesis. By leveraging the instantaneous change-of-variables formula, one can directly…
Inference algorithms based on evolving interactions between replicated solutions are introduced and analyzed on a prototypical NP-hard problem - the capacity of the binary Ising perceptron. The efficiency of the algorithm is examined…
The matrix rank minimization problem has applications in many fields such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization…
Recomi (REpeated COrrelation Matrix Inversion) is a polynomially fast algorithm for searching optimally stable solutions of the perceptron learning problem. For random unbiased and biased patterns it is shown that the algorithm is able to…
Modern programmable digital signal processing relies on floating-point numbers for their ease of use. Fixed-point number formats have the potential to save resources and improve execution time, but realising this potential burdens the…
This article investigates a fast and stable method to solve Henderson's mixed model equation. The proposed algorithm is stable in that it avoids inverting a matrix of a large dimension and hence is free from the curse of dimensionality.…
Piecewise regression is a versatile approach used in various disciplines to approximate complex functions from limited, potentially noisy data points. In control, piecewise regression is, e.g., used to approximate the optimal control law of…
We refine the bit complexity analysis of an algorithm for the computation of at least one point per connected component of a smooth real algebraic set, yielding exponential speedup (with respect to the number of variables) compared to prior…
A new method is introduced for solving Laplace problems on 2D regions with corners by approximation of boundary data by the real part of a rational function with fixed poles exponentially clustered near each corner. Greatly extending a…
Iterative linear solvers have gained recent popularity due to their computational efficiency and low memory footprint for large-scale linear systems. The relaxation method, or Motzkin's method, can be viewed as an iterative method that…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
Using typical solution strategies to compute the solution curve of challenging problems often leads to the break down of the algorithm. To improve the solution process, numerical continuation methods have proved to be a very efficient tool.…