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...

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

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...

We develop a Levenberg-Marquardt method for minimizing the sum of a smooth nonlinear least-squares term \(f(x) = \tfrac{1}{2} \|F(x)\|_2^2\) and a nonsmoo...

This paper presents PDENLPModels.jl a new Julia package for modeling and discretizing optimization problems with mixed algebraic and partial differential equ...

We consider the generalized successive overrelaxation (GSOR) method for solving a class of block three-by-three saddle-point problems. Based on the necessary...

We consider the problem of training a deep neural network with nonsmooth regularization to retrieve a sparse and efficient sub-structure. Our regularizer is ...

The conjugate gradient (CG) method is a classic Krylov subspace method for solving symmetric positive definite linear systems. We introduce an analogous sem...

We describe a procedure to compute a projection of \(w \in ℝ^n\) into the intersection of the so-called zero-norm ball \(k B_0\) of radius \(k\), i....

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...

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...

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...

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...

We study X-ray tomograqphic reconstruction using statistical methods. The problem is expressed in cylindrical coordinates, which yield significant computatio...

Stochastic Dynamic Programming (SDP) is a powerful approach applicable to nonconvex and stochastic stagewise problems. We investigate the impact of the form...

We propose an iterative method named LSLQ for solving linear least-squares problems \(A x \approx b\) of any shape. The method is based on the Golub and K...

For positive definite linear systems (or semidefinite consistent systems), we use Gauss-Radau quadrature to obtain a cheaply computable upper bound on the ...

NLP.py is a programming environment to model continuous optimization problems and to design computational methods in the high-level and powerful Python l...

We describe a collection of linear systems generated during the iterations of an interior-point method for convex quadratic optimization. As the iteration...

Adaptative cubic regularization (ARC) methods for unconstrained optimization compute steps from linear systems with a shifted Hessian in the spirit of the mo...

In many large engineering design problems, it is not computationally feasible or realistic to store Jacobians or Hessians explicitly. Matrix-free implementat...

A preconditioned variant of the Golub and Kahan (1965) bidiagonalization process recently proposed by Arioli (2013) and Arioli and Orban (2013) allows us to ...

We propose a generalization of the limited-memory Cholesky factorization of Lin and Moré (1999) to the symmetric indefinite case with special interest in sym...

Symmetric quasi-definite systems may be interpreted as regularized linear least-squares problem in appropriate metrics and arise from applications such as re...

We describe the most recent evolution of our constrained and unconstrained testing environment and its accompanying SIF decoder. Code-named SIFDecode and CU...

Projected Krylov methods are full-space formulations of Krylov methods that take place in a nullspace. Provided projections into the nullspace can be compute...

Interior-point methods feature prominently among numerical methods for inequality-constrained optimization problems, and involve the need to solve a sequ...

Interior-point methods in semi-definite programming (SDP) require the solution of a sequence of linear systems which are used to derive the search directions...

OPAL is a general-purpose system for modeling and solving algorithm optimization problems. OPAL takes an algorithm as input, and as output it suggests para...

Implementations of the Simplex method differ only in very specific aspects such as the pivot rule. Similarly, most relaxation methods for mixed-integer ...

The analytic center cutting plane method and its proximal variant are well known techniques for solving convex programming problems. We propose two seq...

We consider a class of infeasible, path-following methods for convex quadratric programming. Our methods are designed to be effective for solving both nonde...

We propose an interior-point algorithm based on an elastic formulation of the \(\ell_1\)-penalty merit function for mathematical programs with complementar...

Interior-point methods in augmented form for linear and convex quadratic programming require the solution of a sequence of symmetric indefinite linear ...

Parameterizing source code for architecture-bound optimization is a common approach to high-performance programming but one that makes the programmer's task ...

We propose a modified primal-dual interior-point method for nonlinear programming that relaxes the requirement of closely following the central path and lend...

In the context of algorithmic parameter optimization, there is much room for efficient usage of computational resources. We consider the OPAL framework in wh...

A mixed interior/exterior-point method for nonlinear programming is described, that handles constraints by way of an <i>l</i>₁-penalty function. A...

We introduce the OPAL framework in which the identification of good algorithmic parameters is interpreted as a black box optimization problem whose variables...

This intentionally short tutorial is an introduction to the main features of AMPL that are relevant to nonlinear optimization model authoring. Pointers are g...

The Improved Primal Simplex algorithm IPS [8] is a dynamic constraint reduction method particularly effective on degenerate linear programs. It is able to ac...

We present a procedure for self calibration of a pinhole camera subject to radial distortion. Radial distortion parameters are estimated using a nonlinear le...

We propose a class of projected Krylov methods for the solution of unsymmetric augmented systems of equations such as those arising from the finite-element f...

We describe LANCELOT_simple, an interface to the LANCELOT B nonlinear optimization package within the GALAHAD library (Gould, Orban and Toint, 2003) which ig...

In this paper, we examine sets of tools associated to modeling systems for mathematical programming which can be used to automatically detect the presence ...

We recall the use of squared slacks used to transform inequality constraints into equalities and several reasons why their introduction may be harmful in ...

Optimization problems modeled in the AMPL modeling language [Fourer, Gay and Kernighan (2002)] may be examined by a set of tools found in the AMPL Library [...

We propose a unified framework for the update of the barrier parameter in interiorpoint methods for nonlinear programming. The original primal-dual system i...

The objectives of this paper are twofold; we first demonstrate the flexibility of the mesh adaptive direct search (MADS) in identifying locally optimal algo...

In this paper, we examine the sensitivity of trust-region algorithms on the param- eters related to the step acceptance and update of the trust region. We s...

Recent developments in numerical methods for solving large differentiable nonlinear optimization problems are reviewed. State-of-the-art algorithms for solv...