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

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

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...

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

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 ...

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 ...

We describe LNLQ for solving the least-norm problem \(\min\ \|x\|\) subject to \(Ax=b\). Craig's method is known to be equivalent to applying the conjug...

We propose an infeasible interior-point algorithm for constrained linear least-squares problems based on the primal-dual regularization of convex program...

We propose a factorization-free method for equality-constrained optimization based on a problem in which all constraints are systematically regularized. ...

For optimization problems involving many nonlinear inequality constraints, we extend the bound-constrained (BCL) and linearly-constrained (LCL) augmented-La...

We consider the solution of derivative-free optimization problems with continuous, integer, discrete and categorical variables in the context of costly black...