相关论文: EL-AGHF: Extended Lagrangian Affine Geometric Heat…

We develop a new Lagrangian approach --- flow dynamic approach to effectively capture the interface in the Allen-Cahn type equations. The underlying principle of this approach is the Energetic Variational Approach (EnVarA), motivated by…

This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization…

This article aims to derive a practical tracking control algorithm for flexible air-breathing hypersonic vehicles (FAHVs) with lumped disturbances, unmeasurable states and actuator failures. Based on the framework of the backstepping…

We study a recent timestep adaptation technique for hyperbolic conservation laws. The key tool is a space-time splitting of adjoint error representations for target functionals due to S\"uli and Hartmann. It provides an efficient choice of…

This paper proposes a partially inexact alternating direction method of multipliers for computing approximate solution of a linearly constrained convex optimization problem. This method allows its first subproblem to be solved inexactly…

We discuss general incompressible inviscid models, including the Euler equations, the surface quasi-geostrophic equation, incompressible porous medium equation, and Boussinesq equations. All these models have classical unique solutions, at…

In this paper, we propose an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale structured convex optimization problems. Unlike the exact versions considered in literature,…

This paper develops a primal-dual dynamical system where the coefficients are designed in closed-loop way for solving a convex optimization problem with linear equality constraints. We first introduce a ``second-order primal" +…

This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…

This thesis presents new mathematical algorithms for the numerical solution of a mathematical problem class called \emph{dynamic optimization problems}. These are mathematical optimization problems, i.e., problems in which numbers are…

We examine stability properties of primal-dual gradient flow dynamics for composite convex optimization problems with multiple, possibly nonsmooth, terms in the objective function under the generalized consensus constraint. The proposed…

This paper addresses the three-dimensional path-following guidance problem for unmanned aerial vehicles under explicit actuator constraints. Unlike conventional approaches that assume unbounded control inputs or handle saturation…

In this paper, we propose a variational Lagrangian scheme for a modified phase-field model, which can compute the equilibrium states for the original Allen-Cahn type model. Our discretization is based on a prescribed energy-dissipation law…

In light of the increasing coupling between electricity and gas networks, this paper introduces two novel iterative methods for efficiently solving the multiperiod optimal electricity and gas flow (MOEGF) problem. The first is an iterative…

Fine-grained urban flow inference is crucial for urban planning and intelligent transportation systems, enabling precise traffic management and resource allocation. However, the practical deployment of existing methods is hindered by two…

The Allen-Cahn equation with Flory-Huggins potential is a fundamental and crucial model in phase field simulation for describing phase separation phenomena, which serves as a core tool in diverse branches of natural sciences. The numerical…

This work presents an algorithmic scheme for solving the infinite-time constrained linear quadratic regulation problem. We employ an accelerated version of a popular proximal gradient scheme, commonly known as the Forward-Backward Splitting…

In this paper we consider a non-monotone (mixed) variational inequality model with (nonlinear) convex conic constraints. Through developing an equivalent Lagrangian function-like primal-dual saddle-point system for the VI model in question,…

This paper focuses on the numerical solution of a dual-phase-lag heat conduction equation on a space unbounded domain. First, based on the Laplace transform and the Pad\'e approximation, a high-order local artificial boundary condition is…

A proximal safeguarded augmented Lagrangian method for minimizing the difference of convex (DC) functions over a nonempty, closed and convex set with additional linear equality as well as convex inequality constraints is presented. Thereby,…