Related papers: Tensor Method for Optimal Control Problems Constra…
Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must confront the challenge of controlling errors in the discrete divergence of the magnetic field. One approach that has been…
This paper focusses on the optimal control problems governed by fourth-order linear elliptic equations with clamped boundary conditions in the framework of the Hessian discretisation method (HDM). The HDM is an abstract framework that…
Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bispectrum measurements. We reformulate this nonlin- ear problem as a linear problem for the supersymmetric rank-1…
A method is presented for the numerical solution of optimal boundary control problems governed by parabolic partial differential equations. The continuous space-time optimal control problem is transcribed into a sparse nonlinear programming…
In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…
We consider the problem of recovering a low-multilinear-rank tensor from a small amount of linear measurements. We show that the Riemannian gradient algorithm initialized by one step of iterative hard thresholding can reconstruct an…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
Many scientific and engineering challenges can be formulated as optimization problems which are constrained by partial differential equations (PDEs). These include inverse problems, control problems, and design problems. As a major…
This work considers the problem of approximating initial condition and time-dependent optimal control and trajectory surfaces using multivariable Fourier series. A modified Augmented Lagrangian algorithm for translating the optimal control…
We consider convex optimization problems with the objective function having Lipshitz-continuous $p$-th order derivative, where $p\geq 1$. We propose a new tensor method, which closes the gap between the lower…
In this paper, we study the polynomial optimization problem of multi-forms over the intersection of the multi-spheres and the nonnegative orthants. This class of problems is NP-hard in general, and includes the problem of finding the best…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…
We present a stochastic optimization method that uses a fourth-order regularized model to find local minima of smooth and potentially non-convex objective functions with a finite-sum structure. This algorithm uses sub-sampled derivatives…
We propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution…
This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…
In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data…
Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…
The aim of this work is to study, from an intrinsic and geometric point of view, second-order constrained variational problems on Lie algebroids, that is, optimization problems defined by a cost functional which depends on higher-order…