相关论文: A Conic Model for Electrolyzer Scheduling

Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of…

This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for…

The convex restriction of the power flow feasible sets identifies the convex subset of power injections where the solution for power flow is guaranteed to exist and satisfy the operational constraints. In contrast to convex relaxations, the…

Simulations of large-scale plasma systems are typically based on a fluid approximation approach. These models construct a moment-based system of equations that approximate the particle-based physics as a fluid, but as a result lack the…

The Calder\'on problem consists in recovering an unknown coefficient of a partial differential equation from boundary measurements of its solution. These measurements give rise to a highly nonlinear forward operator. As a consequence, the…

The connection between domain relaxations at individual scales and the collective heterogeneous response in non-equilibrium systems is a topic of profound interest in recent times. In a model sys- tem of constantly driven oppositely charged…

This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations…

Context: Relaxation theory offers a straightforward method for estimating the energy that is released when a magnetic field becomes unstable, as a result of continual convective driving. Aims: We present new results obtained from nonlinear…

This work is concerned with relaxation models arising from numerical schemes for hyperbolic-parabolic systems. Such models are a hyperbolic system with both the hyperbolic part and the stiff source term involving a small positive parameter,…

An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear time-invariant systems but differ in their output equations,…

We introduce a novel technique to generate Benders' cuts from a conic relaxation ("corner") derived from a basis of a higher-dimensional polyhedron that we aim to outer approximate in a lower-dimensional space. To generate facet-defining…

We present a novel methodology for convex optimization algorithm design using ideas from electric RLC circuits. Given an optimization problem, the first stage of the methodology is to design an appropriate electric circuit whose…

In order to increase the efficiency of the computer simulation of biological molecules, it is very common to impose holonomic constraints on the fastest degrees of freedom; normally bond lengths, but also possibly bond angles. However, as…

AC optimal power flow (AC OPF) is a fundamental problem in power system operations. Accurately modeling the network physics via the AC power flow equations makes AC OPF a challenging nonconvex problem. To search for global optima, recent…

This note is devoted to a simple method for proving hypocoercivity of the solutions of a kinetic equation involving a linear time relaxation operator, i.e. the construction of an adapted Lyapunov functional satisfying a Gronwall-type…

Pose Graph Optimization involves the estimation of a set of poses from pairwise measurements and provides a formalization for many problems arising in mobile robotics and geometric computer vision. In this paper, we consider the case in…

A non-extensive (3+1)-dimensional hydrodynamic model for multi-particle production processes, NEX-CLVisc, is developed in the framework of CLVisc where the viscous corrections are turned off. It assumes that the non-extensive effects…

The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic…

We discuss relaxation and aging processes in the one- and two-dimensional $ABC$ models. In these driven diffusive systems of three particle types, biased exchanges in one direction yield a coarsening process characterized in the long time…

Integrated electricity and gas systems are constructed to facilitate the gas-fired generation, and the distributed operation of these integrated systems have received much attention due to the increased emphasis on data security and privacy…