Related papers: Deterministic monotone dynamics and dominated stra…

The design of fixed point algorithms is at the heart of monotone operator theory, convex analysis, and of many modern optimization problems arising in machine learning and control. This tutorial reviews recent advances in understanding the…

In neuroscience, optics and condensed matter there is ample physical evidence for multistable dynamical systems, that is, systems with a large number of attractors. The known mathematical mechanisms that lead to multiple attractors are…

We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…

The paper deals with the study of a Lane-Emden-Fowler equation with Dirichlet boundary condition and variable potential functions. The analysis developed in this paper combines monotonicity methods with variational arguments. Remark (April…

The game theoretic concepts of rationalizability and iterated dominance are closely related and provide characterizations of each other. Indeed, the equivalence between them implies that in a two player finite game, the remaining set of…

Here, we introduce a novel method for obtaining chaotic dynamics based on the Montgomery conjecture for the pair correlation of zeros of the Riemann zeta function. Motivated by the conjecture, we present a recursive relation that reveals…

Dispersal of species to find a more favorable habitat is important in population dynamics. Dispersal rates evolve in response to the relative success of different dispersal strategies. In a simplified deterministic treatment (J. Dockery, V.…

Monotonicity and convex analysis arise naturally in the framework of multi-marginal optimal transport theory. However, a comprehensive multi-marginal monotonicity and convex analysis theory is still missing. To this end we study extensions…

Monotone convex operators and time-consistent systems of operators appear naturally in stochastic optimization and mathematical finance in the context of pricing and risk measurement. We study the dual representation of a monotone convex…

Motivated by recent development in networking and parallel data-processing, we consider a distributed and localized finite-sum (or fixed-sum) allocation technique to solve resource-constrained convex optimization problems over multi-agent…

We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…

As an example of the nonlinear Fokker-Planck equation, the mean field Langevin dynamics recently attracts attention due to its connection to (noisy) gradient descent on infinitely wide neural networks in the mean field regime, and hence the…

Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…

We propose a novel approach to modeling advertising dynamics for a firm operating over distributed market domain based on controlled partial differential equations of diffusion type. Using our model, we consider a general type of…

We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input. The nodes may have either a discrete or continuous set…

This paper investigates the synthesis of distributed economic control algorithms under which dynamically coupled physical systems are regulated to a variational equilibrium of a constrained convex game. We study two complementary cases: (i)…

We adapt the quasi-monotone method from [2] for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is…

We give a generalization and a short mechanized proof of determinant conjectured by G. Kuperberg and J. Propp. Further generalizations and applications of the method to some q-analogues may be found in http://www.math.temple.edu/~tewodros

This paper studies a constrained optimization problem over networked systems with an undirected and connected communication topology. The algorithm proposed in this work utilizes singular perturbation, dynamic average consensus, and saddle…

These lecture notes are derived from a graduate-level course in dynamic optimization, offering an introduction to techniques and models extensively used in management science, economics, operations research, engineering, and computer…