Related papers: Continuous dynamics related to monotone inclusions…
We focus on the solutions of second-order stable linear difference equations and demonstrate that their behavior can be non-monotone and exhibit peak effects depending on initial conditions. The results are applied to the analysis of the…
We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the…
This technical note studies the distributed optimization problem of a sum of nonsmooth convex cost functions with local constraints. At first, we propose a novel distributed continuous-time projected algorithm, in which each agent knows its…
Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…
This paper investigates a specific class of nonsmooth nonconvex optimization problems in the face of data uncertainty, namely, robust optimization problems, where the given objective function can be expressed as a difference of two…
We are interested in existence results for second order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal…
This paper studies the dynamics of families of monotone nonautonomous neutral functional differential equations with nonautonomous operator, of great importance for their applications to the study of the long-term behavior of the…
While many distributed optimization algorithms have been proposed for solving smooth or convex problems over the networks, few of them can handle non-convex and non-smooth problems. Based on a proximal primal-dual approach, this paper…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on properties such as the weak order which estimates the asymptotic…
In this paper we study, from a variational and geometrical point of view, second-order variational problems on Lie groupoids and the construction of variational integrators for optimal control problems. First, we develop variational…
This paper considers continuous-time coordination algorithms for networks of agents that seek to collectively solve a general class of nonsmooth convex optimization problems with an inherent distributed structure. Our algorithm design…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
This paper studies the asymptotic convergence properties of the primal-dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by…