相关论文: Implicit A-Stable Peer Triplets for ODE Constraine…

A class of distributed optimization problem with a globally coupled equality constraint and local constrained sets is studied in this paper. For its special case where local constrained sets are absent, an augmented primal-dual gradient…

The alternating current optimal power flow (AC-OPF) problem is critical to power system operations and planning, but it is generally hard to solve due to its nonconvex and large-scale nature. This paper proposes a scalable decomposition…

In this paper, we discuss the distributed control problem governed by the following parabolic integro-differential equation (PIDE) in the abstract form \begin{eqnarray*} \frac{\partial y}{\partial t} + A y &=& \int_0^t B(t, s) y(s) ds + Gu,…

In this paper, a new implicit-explicit local method with an arbitrary order is produced for stiff initial value problems. Here, a general method for one-step time integrations has been created, considering a direction free approach for…

Stiff systems of ordinary differential equations (ODEs) are pervasive in many science and engineering fields, yet standard neural ODE approaches struggle to learn them. This limitation is the main barrier to the widespread adoption of…

This paper considers a two-step fourth-order modified explicit Euler/Crank-Nicolson numerical method for solving the time-variable fractional mobile-immobile advection-dispersion model subjects to suitable initial and boundary conditions.…

This paper studies fully discrete finite element approximations to the Navier-Stokes equations using inf-sup stable elements and grad-div stabilization. For the time integration two implicit-explicit second order backward differentiation…

In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…

We propose the first general and scalable framework to design certifiable algorithms for robust geometric perception in the presence of outliers. Our first contribution is to show that estimation using common robust costs, such as truncated…

In this study, we focus on the numerical solution method for the optimal control problem with equilibrium constraints (OCPEC).It is extremely challenging to solve OCPEC owing to the absence of constraint regularity and strictly feasible…

A new class of fully decoupled consistent splitting schemes for the Navier-Stokes equations are constructed and analyzed in this paper. The schemes are based on the Taylor expansion at $t^{n+\beta}$ with $\beta\ge 1$ being a free parameter.…

We study the problem of optimal state-feedback tracking control for unknown discrete-time deterministic systems with input constraints. To handle input constraints, state-of-art methods utilize a certain nonquadratic stage cost function,…

This paper focuses on an AC optimal power flow (OPF) problem for distribution feeders equipped with controllable distributed energy resources (DERs). We consider a solution method that is based on a continuous approximation of the projected…

We deduce stability results for finite control set and mixed-integer model predictive control with a downstream oversampling phase. The presentation rests upon the inherent robustness of model predictive control with stabilizing terminal…

This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system…

In this paper, we study a fixed-confidence, fixed-tolerance formulation of a class of stochastic bi-level optimization problems, where the upper-level problem selects from a finite set of systems based on a performance metric, and the…

Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…

Motivated by applications in Optimization, Game Theory, and the training of Generative Adversarial Networks, the convergence properties of first order methods in min-max problems have received extensive study. It has been recognized that…

In order to be convergent, linear multistep methods must be zero stable. While constant step size theory was established in the 1950's, zero stability on nonuniform grids is less well understood. Here we investigate zero stability on…

In this study, we propose high-order implicit and semi-implicit schemes for solving ordinary differential equations (ODEs) based on Taylor series expansion. These methods are designed to handle stiff and non-stiff components within a…