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We leverage path differentiability and a recent result on nonsmooth implicit differentiation calculus to give sufficient conditions ensuring that the solution to a monotone inclusion problem will be path differentiable, with formulas for…
The motivation of this work stems from the numerical approximation of bounded functions by polynomials satisfying the same bounds. The present contribution makes use of the recent algebraic characterization found in [B. Despr\'es, Numer.…
In the context of dynamical systems, nonlinearity measures quantify the strength of nonlinearity by means of the distance of their input-output behaviour to a set of linear input-output mappings. In this paper, we establish a framework to…
In view of the minimization of a function which is the sum of a differentiable function $f$ and a convex function $g$ we introduce descent methods which can be viewed as produced by inexact auxiliary problem principleor inexact variable…
A symbolic computational algorithm which detects " linear "` solutions of nonlinear polynomial differential equations of single functions, is developed throughout this paper.
We consider a one-dimensional gradient symmetric exclusion process in mild contact with boundary reservoirs. The hydrodynamic limit of the empirical measure is given by a non-linear second-order parabolic equation with non-linear Robin…
We consider the semi-infinite optimization problem: $f^*:=\min_{x\in X}\:\{f(x): g(x,y)\,\leq \,0,\:\forally\in Y_x\}$, where $f,g$ are polynomials and $X\subset R^n$ as well as $Y_\x\subset R^p$, $x\in X$, are compact basic semi-algebraic…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…
We consider the problem of minimizing a fixed-degree polynomial over the standard simplex. This problem is well known to be NP-hard, since it contains the maximum stable set problem in combinatorial optimization as a special case. In this…
Polynomial and rational functions are the number one choice when it comes to modeling of radial distortion of lenses. However, several extrapolation and numerical issues may arise while using these functions that have not been covered by…
The auxiliary function method allows computation of extremal long-time averages of functions of dynamical variables in autonomous nonlinear ordinary differential equations via convex optimization. For dynamical systems defined by autonomous…
Computer algebra can answer various questions about partial differential equations using symbolic algorithms. However, the inclusion of data into equations is rare in computer algebra. Therefore, recently, computer algebra models have been…
We propose a new method for solution of the integrability problem for evolutionary differential-difference equations of arbitrary order. It enables us to produce necessary integrability conditions, to determine whether a given equation is…
For a quadratic matrix polynomial dependent on parameters and a given tolerance $\epsilon > 0$, the minimization of the $\epsilon$-pseudospectral abscissa over the set of permissible parameter values is discussed, with applications in…
Let $\bbK$ be an ordinary differential field with derivation $\partial$. Let $\cP$ be a system of $n$ linear differential polynomial parametric equations in $n-1$ differential parameters with implicit ideal $\id$. Given a nonzero linear…
We introduce the parametric matroid one-interdiction problem. Given a matroid, each element of its ground set is associated with a weight that depends linearly on a real parameter from a given parameter interval. The goal is to find, for…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
Computing the invariant probability measure of a randomly perturbed dynamical system usually means solving the stationary Fokker-Planck equation. This paper studies several key properties of a novel data-driven solver for low-dimensional…
In dynamical systems governed by differential equations, a guarantee that trajectories emanating from a given set of initial conditions do not enter another given set can be obtained by constructing a barrier function that satisfies certain…