相关论文: The Tallest Column -- A Dynamical System Approach …

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…

In this paper, we propose a distributed computing approach to solving large-scale robust stability problems on the simplex. Our approach is to formulate the robust stability problem as an optimization problem with polynomial variables and…

Proposed is a new formal approach for solution of extreme multi-criteria problems transforming them into single-criterion mathematical models, without any additional information. Transforming rules are based on comparison standards and…

A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…

This paper is concerned with the optimal control problem governed by a linear parabolic equation and subjected to box constraints on control variables. This type of problem has important applications in heating and cooling systems. By…

Simple cardinality refers to counting nonzero elements of an independent variable satisfying certain properties. Composite cardinality is a simple counting process composited with an affine mapping, and is therefore more complicated than…

A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…

Massively parallel hardware (GPUs) and long sequence data have made parallel algorithms essential for machine learning at scale. Yet dynamical systems, like recurrent neural networks and Markov chain Monte Carlo, were thought to suffer from…

We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…

In the current industry, the development of optimized mechanical components able to satisfy the customer requirements evolves quickly. Therefore, companies are asked for efficient solutions to improve their products in terms of stiffness…

Many challenging tasks in sensor networks, including sensor calibration, ranking of nodes, monitoring, event region detection, collaborative filtering, collaborative signal processing, {\em etc.}, can be formulated as a problem of solving a…

We introduce a two-phase approximation method designed to resolve singularities in three-dimensional harmonic Dirichlet problems. The approach utilizes the classical Green's function representation, decomposing the function into its…

In this paper, we mainly study solution uniqueness of some convex optimization problems. Our characterizations of solution uniqueness are in terms of the radial cone. This approach allows us to know when a unique solution is a strong…

Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…

We show how clustering as a general hierarchical dynamical process proceeds via a sequence of inverse cascades to produce self-similar scaling, as an intermediate asymptotic, which then truncates at the largest spatial scales. We show how…

We address a class of systems for which the solution to an H-infinity optimal control problem can be given on a very simple closed form. In fact, both the control law and optimal performance value are explicitly given. The class of systems…

We consider a class of relaxation problems mixing slow and fast variations which can describe population dynamics models or hyperbolic systems, with varying stiffness (from non-stiff to strongly dissipative), and develop a multi-scale…

In this paper we investigate the discrete version of the classical hanging chain problem. We generalize the problem, by allowing for arbitrary mass and length of each link. We show that the shape of the chain can be obtained by solving a…

The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…

We aim to solve a topology optimization problem where the distribution of material in the design domain is represented by a density function. To obtain candidates for local minima, we want to solve the first order optimality system via…