This paper presents DCISolver.jl a new Julia package implementating the Dynamic Control of Infeasibility method (DCI), introduced by Bielschowsky & Gomes (20...

We introduce an iterative method named GPMR for solving 2X2 block unsymmetric linear systems. GPMR is based on a new process that reduces simultaneously...

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...

In this paper, we consider both first- and second-order techniques to address continuous optimization problems arising in machine learning. In the first-orde...

We introduce iterative methods named TriCG and TriMR for solving symmetric quasi-definite systems based on the orthogonal tridiagonalization process proposed...

We describe a Julia implementation of Mehrotra's predictor-corrector method for convex quadratic optimization that is entirely open source and generic in tha...

Algorithm NCL is designed for general smooth optimization problems
    where first and second derivatives are available,
    including problems whose constrai...

We propose a new stochastic variance-reduced damped L-BFGS algorithm, where we leverage estimates of bounds on the largest and smallest eigenvalues of the He...

We present a modeling of bundle adjustment problems in Julia, as well as a solver for non-linear least square problems (including bundle adjustment problems)...

We consider the iterative solution of regularized saddle-point systems. When the leading block is symmetric and positive semi-definite on an appropriate sub...

We provide eigenvalues bounds for a new formulation of the step equations in interior methods for convex quadratic optimization. The matrix of our formulati...

Artificial Intelligence (AI) is the next society transformation builder. Massive AI-based applications include cloud servers, cell phones, cars, and pandemic...

In this paper, we compare the BFGS and the conjugate gradient (CG) methods for solving unconstrained problems with a trust-region algorithm. The main result ...

We introduce an iterative method named BiLQ for solving general square linear systems \(Ax=b\) based on the Lanczos biorthogonalization process defined by ...

Statistical image reconstruction in X-Ray computed tomography yields large-scale regularized linear least-squares problems with nonnegativity bounds, where t...

We build upon Estrin et al. (2019) to develop a general constrained nonlinear optimization algorithm based on a smooth penalty function proposed by Fletch...

The minimum residual method (MINRES) of Paige and Saunders (1975), which is often the method of choice for symmetric linear systems, is a generalization of t...

We propose an iterative method named USYMLQR for the solution of symmetric saddle-point systems that exploits the orthogonal tridiagonalization method of Sa...

We propose a regularization method for nonlinear least-squares problems with equality constraints. Our approach is modeled after those of Arreckx and Orban ...

We develop a general equality-constrained nonlinear optimization algorithm based on a smooth penalty function proposed by Fletcher (1970). Although it was ...