相关论文: An overlapping waveform-relaxation preconditioner …

Training learned image compression (LIC) models entails navigating a challenging optimization landscape defined by the fundamental trade-off between rate and distortion. Standard first-order optimizers, such as SGD and Adam, struggle with…

We present here the classical Schwarz method with a time domain decomposition applied to unconstrained parabolic optimal control problems. Unlike Dirichlet-Neumann and Neumann-Neumann algorithms, we find different properties based on the…

In this paper, we consider the exact boundary controllability and the exact boundary synchronization (by groups) for a coupled system of wave equations with coupled Robin boundary controls. Owing to the difficulty coming from the lack of…

We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…

We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the…

We explore computational aspects of maximum likelihood estimation of the mixture proportions of a nonparametric finite mixture model -- a convex optimization problem with old roots in statistics and a key member of the modern data analysis…

In this paper, preconditioning the saddle point problem arising from the elliptic boundary optimal control problem with mixed boundary conditions is considered. A block triangular reconditioning method is proposed based on permutations of…

This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…

Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual…

We consider the problem of stabilization of a linear system, under state and control constraints, and subject to bounded disturbances and unknown parameters in the state matrix. First, using a simple least square solution and available…

This work addresses an optimal control problem for a semilinear elliptic equation in two-dimensional space, characterized by an exponential nonlinearity and a singular source term. The source is modeled as a finite linear combination of…

Pumped at approximately twice the natural frequency, a Josephson parametric oscillator called parametron or Kerr parametric oscillator shows self-oscillation. Quantum annealing and universal quantum computation using self-oscillating…

We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and…

This paper considers a set of multiple independent control systems that are each connected over a non-stationary wireless channel. The goal is to maximize control performance over all the systems through the allocation of transmitting power…

The block structure of double saddle-point problems has prompted extensive research into efficient preconditioners. This paper introduces a novel class of three-by-three block preconditioners tailored for such systems from the…

We consider a parabolic problem with Robin boundary condition which arises when the edge of a micro-electro-mechanical-system (MEMS) device is connected with a flexible nonideal support. Then via a rigorous analysis we investigate the…

In this work we present an adaptive Newton-type method to solve nonlinear constrained optimization problems in which the constraint is a system of partial differential equations discretized by the finite element method. The adaptive…

At the heart of Newton based optimization methods is a sequence of symmetric linear systems. Each consecutive system in this sequence is similar to the next, so solving them separately is a waste of computational effort. Here we describe…

In this paper we deal with the well-posedness of Dirichlet problems associated to nonlocal Hamilton-Jacobi parabolic equations in a bounded, smooth domain $\Omega$, in the case when the classical boundary condition may be lost. We address…

A theoretical framework and numerical techniques to solve optimal control problems with a spatial trace term in the terminal cost and governed by regularized nonlinear hyperbolic conservation laws are provided. Depending on the spatial…