Related papers: Nonstandard Tools for Nonsmooth Analysis

Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological, mechanical, and transportation systems. Thus…

Estimating the state of a dynamical system from a series of noise-corrupted observations is fundamental in many areas of science and engineering. The most well-known method, the Kalman smoother (and the related Kalman filter), relies on…

Short nonstandard proofs are given for some results about infinite systems of equations in infinitely many variables.

We will present the benefits of using methods of non-standard analysis in dynamic projective geometry. One major application will be the desingulariazation of geometric constructions.

We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…

We present new methods for solving a broad class of bound-constrained nonsmooth composite minimization problems. These methods are specially designed for objectives that are some known mapping of outputs from a computationally expensive…

The wide application of estimation techniques in system analysis enable us to best determine and understand the history of system states. This paper attempts to delineate the theory behind linear and non-linear estimation with a suitable…

Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological, mechanical, and transportation systems. The…

This paper is a survey of methods for solving smooth (strongly) monotone stochastic variational inequalities. To begin with, we give the deterministic foundation from which the stochastic methods eventually evolved. Then we review methods…

In this paper, nonstandard multistep methods are considered. It is shown that under some (sufficient and necessary) conditions, these methods attain the same order as their standard counterparts - to prove this statement, a nonstandard…

We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…

We consider the problem of asymptotic convergence to invariant sets in interconnected nonlinear dynamic systems. Standard approaches often require that the invariant sets be uniformly attracting. e.g. stable in the Lyapunov sense. This,…

We present a comprehensive framework for evaluating line chart smoothing methods under a variety of visual analytics tasks. Line charts are commonly used to visualize a series of data samples. When the number of samples is large, or the…

We develop a model reduction technique for non-smooth dynamical systems using spectral submanifolds. Specifically, we construct low-dimensional, sparse, nonlinear and non-smooth models on unions of slow and attracting spectral submanifolds…

In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…

Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized…

We determine sufficient structure for an elementary topos to emulate E. Nelson's Internal Set Theory in its internal language, and show that any topos satisfying the internal axiom of choice occurs as a universe of standard objects and…

The main goal of this paper is developing the method of discrete approximations to derive necessary optimality conditions for a class of constrained sweeping processes with nonsmooth perturbations. Optimal control problems for sweeping…

We extend the theory of ergodic optimization and maximizing measures to the non-commutative field of C*-dynamical systems. We then provide a result linking the ergodic optimizations of elements of a C*-dynamical system to the convergence of…

We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…