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We present an analysis and numerical study of an optimal control problem for the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs), which is a crucial component in modern technology. They exhibit long range orientational order…

This paper is concerned with augmented Lagrangian methods for the treatment of fully convex composite optimization problems. We extend the classical relationship between augmented Lagrangian methods and the proximal point algorithm to the…

Policy gradient (PG) methods are the backbone of many reinforcement learning algorithms due to their good performance in policy optimization problems. As a gradient-based approach, PG methods typically rely on knowledge of the system…

We consider spectral discretizations of hyperbolic problems on unbounded domains using Laguerre basis functions. Taking as model problem the scalar advection equation, we perform a comprehensive stability analysis that includes strong…

We propose a direct numerical method for the solution of an optimal control problem governed by a two-side space-fractional diffusion equation. The presented method contains two main steps. In the first step, the space variable is…

In this paper, we present a stable and efficient approach for constructing Laguerre pseudospectral differentiation matrices. The proposed method reformulates the off-diagonal entries and computes all required quantities simultaneously using…

The work reported in this article presents a high-order, stable, and efficient Gegenbauer pseudospectral method to solve numerically a wide variety of mathematical models. The proposed numerical scheme exploits the stability and the…

Well-conditioned spectral collocation and spectral methods have recently been proposed to solve differential equations. In this paper, we revisit the well-conditioned spectral collocation methods proposed in [T.~A. Driscoll, {\it J. Comput.…

LSQR, a Lanczos bidiagonalization based Krylov subspace iterative method, and its mathematically equivalent CGLS applied to normal equations system, are commonly used for large-scale discrete ill-posed problems. It is well known that LSQR…

The $hp$ local discontinuous Galerkin (LDG) method proposed by Castillo et al. [Math. Comp.,~71 (238): 455-478, 2002] has been shown to be an efficient approach for solving convection-diffusion equations. However, theoretical analysis…

This paper presents two new techniques relating to inexact solution of subproblems in augmented Lagrangian methods for convex programming. The first involves combining a relative error criterion for solution of the subproblems with over- or…

For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods sequentially minimize a Lagrangian function subject to linearized constraints. These methods converge rapidly near a solution but may not be…

This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…

In this work, we consider the construction of efficient surrogates for the stochastic version of the Landau-Lifshitz-Gilbert (LLG) equation using model order reduction techniques, in particular, the Reduced Basis (RB) method. The Stochastic…

Embedding parameterized optimization problems as layers into machine learning architectures serves as a powerful inductive bias. Training such architectures with stochastic gradient descent requires care, as degenerate derivatives of the…

This work investigates the convergence behavior of augmented Lagrangian methods (ALMs) when applied to convex optimization problems that may be infeasible. ALMs are a popular class of algorithms for solving constrained optimization…

This paper introduces a new accurate model for periodic fractional optimal control problems (PFOCPs) using Riemann-Liouville (RL) and Caputo fractional derivatives (FDs) with sliding fixed memory lengths. The paper also provides a novel…

We present a lazy incremental search algorithm, Lifelong-GLS (L-GLS), along with its bounded suboptimal version, Bounded L-GLS (B-LGLS) that combine the search efficiency of incremental search algorithms with the evaluation efficiency of…

We present a method to approximately solve general instances of combinatorial optimization problems using the physical dynamics of 3d rotors obeying Landau-Lifshitz-Gilbert dynamics. Conventional techniques to solve discrete optimization…

For the large-scale linear discrete ill-posed problem $\min\|Ax-b\|$ or $Ax=b$ with $b$ contaminated by white noise, the Golub-Kahan bidiagonalization based LSQR method and its mathematically equivalent CGLS, the Conjugate Gradient (CG)…