Related papers: Second-Order Newton-Based Extremum Seeking for Mul…
The Navier Stokes equations (NSEs) are partial differential equations (PDEs) to describe the nonlinear convective motion of fluids and they are computationally expensive to simulate because of their high nonlinearity and variables being…
Constrained second-order convex optimization algorithms are the method of choice when a high accuracy solution to a problem is needed, due to their local quadratic convergence. These algorithms require the solution of a constrained…
This paper studies the joint support recovery of similar sparse vectors on the basis of a limited number of noisy linear measurements, i.e., in a multiple measurement vector (MMV) model. The additive noise signals on each measurement vector…
A class of second-order algorithms is proposed for minimizing smooth nonconvex functions that alternates between regularized Newton and negative curvature steps in an iteration-dependent subspace. In most cases, the Hessian matrix is…
This work proposes a universal and adaptive second-order method for minimizing second-order smooth, convex functions. Our algorithm achieves $O(\sigma / \sqrt{T})$ convergence when the oracle feedback is stochastic with variance $\sigma^2$,…
Hedging exotic options in presence of market frictions is an important risk management task. Deep hedging can solve such hedging problems by training neural network policies in realistic simulated markets. Training these neural networks may…
Escaping saddle points is a central research topic in nonconvex optimization. In this paper, we propose a simple gradient-based algorithm such that for a smooth function $f\colon\mathbb{R}^n\to\mathbb{R}$, it outputs an…
This paper presents the design and analysis of the extremum seeking for static maps with input passed through a partial differential equation (PDE) of the diffusion type defined on a time-varying spatial domain whose boundary position is…
Sonar systems are frequently used to classify objects at a distance by using the structure of the echoes of acoustic waves as a proxy for the object's shape and composition. Traditional synthetic aperture processing is highly effective in…
An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…
The paper discusses the improvement of the accuracy of an inertial navigation system created on the basis of MEMS sensors using machine learning (ML) methods. As input data for the classifier, we used infor-mation obtained from a developed…
The second-order statistics (SOS) can be applied in estimation of the pure spectra of chemical components from the spectrum of their mixture, when SOS seems to be good at estimation of spectral patterns, but their peak directions are…
Minimizing loss functions is central to machine-learning training. Although first-order methods dominate practical applications, higher-order techniques such as Newton's method can deliver greater accuracy and faster convergence, yet are…
In the inverse problem in particle physics, given an unexpected observation, one aims to identify a unique choice from amongst several competing hypotheses. We explore a novel approach of applying self-organizing maps to the inverse problem…
We propose a multi-objective global pattern search algorithm for the task of locating and quantifying damage in flexible mechanical structures. This is achieved by identifying eigenfrequencies and eigenmodes from measurements and matching…
Graph Neural Networks (GNNs) with equivariant properties have emerged as powerful tools for modeling complex dynamics of multi-object physical systems. However, their generalization ability is limited by the inadequate consideration of…
A crucial step in planet hunting surveys is to select the best candidates for follow up observations, given limited telescope resources. This is often performed by human `eyeballing', a time consuming and statistically awkward process. Here…
We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…
The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…
In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…