Related papers: Relaxed commutant lifting: existence of a unique s…
In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…
We obtain sufficient conditions for the uniqueness of solutions to the Cauchy problem for the continuity equation in classes of measures that need not be absolutely continuous.
The recently-introduced relaxation approach for Runge-Kutta methods can be used to enforce conservation of energy in the integration of Hamiltonian systems. We study the behavior of implicit and explicit relaxation Runge-Kutta methods in…
We present a novel complex number formulation along with tight convex relaxations for the aircraft conflict resolution problem. Our approach combines both speed and heading control and provides global optimality guarantees despite…
Numerous pivotal concepts have been introduced to clarify the puzzle of relaxation and/or equilibration in closed quantum systems. All of these concepts rely in some way on specific conditions on Hamiltonians $H$, observables $A$, and…
The necessary and sufficient condition of separability of a mixed state of any systems is presented, which is practical in judging the separability of a mixed state. This paper also presents a method of finding the disentangled…
Problems involving rolling without slipping or no sideways skidding, to name a few, introduce velocity-dependent constraints that can be efficiently treated by the method of Lagrange multipliers in the Lagrangian formulation of the…
We consider the asymmetric simple exclusion process with Langmuir kinetics in the closed boundary condition. We analytically obtain the exact stationary state and a series of excited states of the system in the limit where Langmuir kinetics…
We discuss the mechanism of truncations driven by the imposition of constraints. We show how the consistency of such truncations is controlled, and give general theorems that establish conditions for the correct uplifting of solutions. We…
Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that…
We analyze the procedure of lifting in classical stochastic and quantum systems. It enables one to `lift' a state of a system into a state of `system+reservoir'. This procedure is important both in quantum information theory and the theory…
We present explicit sufficient conditions that guarantee the existence and uniqueness of the feasible load-flow solution for distribution networks with a generic topology (radial or meshed) modeled with positive sequence equivalents. In the…
This paper proposes a bilevel hierarchy of strengthened complex moment relaxations for complex polynomial optimization. The key trick entails considering a class of positive semidefinite conditions that arise naturally in characterizing the…
Our aim in this paper is to study the Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. In particular, we prove, owing to proper approximations of the singular potential and a suitable notion of variational…
Simple conditions have been developed in [Zhang, Wahl and Yu, SIAM Rev. 2014; Yu and Wang, Math. Biosci. Eng. 2019], which are used to identify the existence of slow-fast relaxation oscillations that appear in differential systems, where…
We prove that the standard conditions that provide unique solvability of a mixed stochastic differential equations also guarantee that its solution possesses finite moments. We also present conditions supplying existence of exponential…
This paper presents a selected tour through the theory and applications of lifts of convex sets. A lift of a convex set is a higher-dimensional convex set that projects onto the original set. Many convex sets have lifts that are…
In this paper, the existence and uniqueness of solution of a specific differential equation is studied. This equation originates from the description of a coupled process by totally asymmetric simple exclusion process (TASEP) and Langmuir…
We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient…