Related papers: Convergence problems in nonlocal dynamics with non…
Our work is motivated by a desire to study the theoretical underpinning for the convergence of stochastic gradient type algorithms widely used for non-convex learning tasks such as training of neural networks. The key insight, already…
This paper is concerned with the long-time dynamics of semilinear wave equation subject to dissipative boundary condition. To do so, we first analyze the set of equilibria, and show it could contain infinitely many elements. Second, we show…
This paper develops a comprehensive convergence analysis for generic classes of descent algorithms in nonsmooth and nonconvex optimization under several conditions of the Polyak-\L ojasiewicz-Kurdyka (PLK) type. Along other results, we…
Optimization algorithms for solving nonconvex inverse problem have attracted significant interests recently. However, existing methods require the nonconvex regularization to be smooth or simple to ensure convergence. In this paper, we…
In the given article the necessary and sufficient conditions of the existence of solutions of boundary value problem for the nonlinear system in the Hilbert spaces are obtained. Examples of such systems like a Lotka-Volterra are considered.…
This article is devoted to presenting an abstract theory on time-fractional gradient flows for nonconvex energy functionals in Hilbert spaces. Main results consist of local and global in time existence of (continuous) strong solutions to…
Real ecosystems are characterized by sparse and asymmetric interactions, posing a major challenge to theoretical analysis. We introduce a new method to study the generalized Lotka-Volterra model with stochastic dynamics on sparse graphs. By…
Solutions of optimization problems, including policy optimization in reinforcement learning, typically rely upon some variant of gradient descent. There has been much recent work in the machine learning, control, and optimization…
In this paper we elaborate on the structure of the Generalized Lotka-Volterra (GLV) form for nonlinear differential equations. We discuss here the algebraic properties of the GLV family, such as the invariance under quasimonomial…
Our recent work lays out a general framework for inferring information about the parameters and associated dynamics of a differential equation model from a discrete set of data points collected from the system being modeled. Rigorous…
We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a…
We consider stochastic differential equations in a Hilbert space, perturbed by the gradient of a convex potential. We investigate the problem of convergence of a sequence of such processes. We propose applications of this method to…
We propose a novel analysis framework for non-descent-type optimization methodologies in nonconvex scenarios based on the Kurdyka-Lojasiewicz property. Our framework allows covering a broad class of algorithms, including those commonly…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
We examine a class of stochastic differential inclusions involving multiscale effects designed to solve a class of generalized variational inequalities. This class of problems contains constrained convex non-smooth optimization problems,…
We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on…
We investigate the convergence of McKean-Vlasov diffusions in a nonconvex landscape. These processes are linked to nonlinear partial differential equations. According to our previous results, there are at least three stationary measures…
For years, a main focus of ecological research has been to better understand the complex dynamical interactions between species which comprise food webs. Using the connectance properties of a widely explored synthetic food web called the…
Non-local continuity equation describes an infinite system of identical particles, which interact with each other through the common field. Solution of this equation is a probability measure that stands for spatial distribution of…
We study a diffusive Lotka-Volterra competition system with advection under Neumann boundary conditions. Our system models a competition relationship that one species escape from the region of high population density of their competitors in…