Related papers: Sensitivity Analysis for Periodic Orbits and Quasi…
Two classes of two-dimensional time-periodic systems of ordinary differential equations with a small parameter e in the perturbed part, which is continuous and, for $\varepsilon=0$, analytic in zero, are studied. Depending on the presence…
Quasi-periodic motions on invariant tori of an integrable system of dimension smaller than half the phase space dimension may continue to exists after small perturbations. The parametric equations of the invariant tori can often be computed…
We give a simple proof of Kolmogorov's theorem on the persistence of a quasiperiodic invariant torus in Hamiltonian systems. The theorem is first reduced to a well-posed inversion problem (Herman's normal form) by switching the frequency…
This work studies existence and regularity questions for attracting invariant tori in three dimensional dissipative systems of ordinary differential equations. Our main result is a constructive method of computer assisted proof which…
The paper addresses the tolerance approach to the sensitivity analysis of optimal solutions to the nonlinear optimization problem of the form $$\mbox{$\bigoplus\limits_{y\in S}C(y)\to\min$\quad over\quad $S\in\mathcal{S}$,}$$ where…
The use of adjoint solvers is considered in order to obtain the sensitivity of clinical measures in aneurysms to incomplete (or unknown) boundary conditions and/or geometry. It is shown that these techniques offer interesting theoretical…
The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…
We consider time-invariant nonlinear $n$-dimensional strongly $2$-cooperative systems, that is, systems that map the set of vectors with up to weak sign variation to its interior. Strongly $2$-cooperative systems enjoy a strong…
We consider the problem of the continuation with respect to a small parameter $\epsilon$ of spatially localised and time periodic solutions in 1-dimensional dNLS lattices, where $\epsilon$ represents the strength of the interaction among…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
Meta-optics promises compact, high-performance imaging and color routing. However, designing high-performance structures is a high-dimensional optimization problem: mapping a desired optical output back to a physical 3D structure requires…
We present a new analytic study of the equilibrium and stability properties of close binary systems containing polytropic components. Our method is based on the use of ellipsoidal trial functions in an energy variational principle. We…
We consider autonomous Hamiltonian systems and present an algorithm to compute at the same time partially hyperbolic invariant tori (whiskered tori), as well as high-order expansions of their stable and unstable manifolds. Such whiskered…
Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of general boundary value problems for these systems is formulated in the sense of…
We propose a novel non-linear extension to the Orienteering Problem (OP), called the Correlated Orienteering Problem (COP). We use COP to model the planning of informative tours for the persistent monitoring of a spatiotemporal field with…
In this paper, we accomplish a unified convergence analysis of a second-order method of multipliers (i.e., a second-order augmented Lagrangian method) for solving the conventional nonlinear conic optimization problems.Specifically, the…
This article reviews several recently developed Lagrangian tools and shows how their combined use succeeds in obtaining a detailed description of purely advective transport events in general aperiodic flows. In particular, because of the…
This work introduces the use of the Koopman operator theory to generate approximate analytical solutions for the zonal harmonics problem of a satellite orbiting a non-spherical celestial body. Particularly, the solution proposed directly…