Related papers: A note on stability and optimal approximation esti…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing…
This paper presents a robust, distributed algorithm to solve general linear programs. The algorithm design builds on the characterization of the solutions of the linear program as saddle points of a modified Lagrangian function. We show…
In this work, we consider a time-varying stochastic saddle point problem in which the objective is revealed sequentially, and the data distribution depends on the decision variables. Problems of this type express the distributional…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems…
A methodology on making the variational principle well-posed in degenerate systems is constructed. In the systems including higher-order time derivative terms being compatible with Newtonian dynamics, we show that a set of position…
In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…
This paper investigates the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for solving monotone variational inequality problems. The exact worst case convergence rate is computed using the performance…
This paper deals with the generalized spectrum of continuously invertible linear operators defined on infinite dimensional Hilbert spaces. More precisely, we consider two bounded, coercive, and self-adjoint operators $\bc{A, B}: V\mapsto…
This paper discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its original form, may produce erratic results or diverge because of…
The stability of an approximating sequence $(A_n)$ for an operator $A$ usually requires, besides invertibility of $A$, the invertibility of further operators, say $B, C, \dots$, that are well-associated to the sequence $(A_n)$. We study…
We present a comprehensive theoretical analysis of first-order methods for escaping strict saddle points in smooth non-convex optimization. Our main contribution is a Perturbed Saddle-escape Descent (PSD) algorithm with fully explicit…
The objective of this paper is to report some computational results for the theory of DAE stability boundary, with the aim of advancing applications in power system voltage stability studies. Firstly, a new regularization transformation for…
We establish the optimal nonergodic sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. First, the optimal bound is formulated by the performance estimation framework, resulting in an infinite…
We consider the rate of piecewise constant approximation to a locally stationary process $X(t),t\in [0,1]$, having a variable smoothness index $\alpha(t)$. Assuming that $\alpha(\cdot)$ attains its unique minimum at zero and satisfies the…
We study the backstepping stabilization of higher order linear and nonlinear Schr\"odinger equations on a finite interval, where the boundary feedback acts from the left Dirichlet boundary condition. The plant is stabilized with a…
We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
In this work, we conduct a systematic study of stochastic saddle point problems (SSP) and stochastic variational inequalities (SVI) under the constraint of $(\epsilon,\delta)$-differential privacy (DP) in both Euclidean and non-Euclidean…