Algorithm NCL was devised to solve a class of large nonlinearly constrained optimization problems whose constraints do not satisfy LICQ at a solution. It ...

We propose a multi-precision extension of the Quadratic Regularization (R2) algorithm that enables it to take advantage of low-precision computations, and by...

We develop a worst-case evaluation complexity bound for trust-region methods in the presence of unbounded Hessian approximations. We use the algorithm of ...

We explore a scaled spectral preconditioner for the efficient solution of sequences of symmetric and positive-definite linear systems. We design the scaled...

Penalty methods are a well known class of algorithms for constrained optimization. They transform a constrained problem into a sequence of unconstrained _pe...

We develop R2N, a modified quasi-Newton method for minimizing the sum of a $\mathcal{C}^1$ function $f$ and a lower semi-continuous prox-bounded `(h...

JSOSuite.jl is a new Julia package offering a user-friendly interface for continuous nonlinear optimization. The solvers available cover unconstrained to g...

We extend traditional complexity analyses of trust-region methods for unconstrained, possibly nonconvex, optimization. Whereas most complexity analyses as...

We describe the implementation of RipQP, an interior-point algorithm for convex quadratic optimization. Our Julia implementation is open source, and accommo...

Augmented Lagrangian (AL) methods are a well known class of algorithms for solving constrained optimization problems. They have been extended to the solution...

The purpose of the present note is to bring clarifications to certain concepts and surrounding notation of Aravkin et al. (2022). All results therein contin...

We develop a trust-region method for minimizing the sum of a smooth term $f$ and a nonsmooth term $h$, both of which can be nonconvex. Each iteratio...

We develop an interior-point method for nonsmooth regularized bound-constrained optimization problems. Our method consists of iteratively solving a sequence...

The Harwell Subroutine Library (HSL) is a renowned suite of efficient and robust numerical algorithms designed to tackle complex mathematical problems such a...

Improving neural network optimizer convergence speed is a long-standing priority. Recently, there has been a focus on quasi-Newton optimization methods, whi...

Historically, the training of deep artificial neural networks has relied on parallel computing to achieve practical effectiveness. However, with the increas...

We introduce an iterative solver named MINARES for symmetric linear systems $Ax \approx b$, where $A$ is possibly singular. MINARES is based on t...

We introduce a variant of the proximal gradient method in which the quadratic term is diagonal but may be indefinite, and is safeguarded by a trust region. ...

We present a Julia framework dedicated to partially-separable problems whose element function are detected automatically. This framework takes advantage of ...

This paper presents $\texttt{Krylov.jl}$, a Julia package that implements a collection of Krylov processes and methods for solving a variety of linear pr...