# Dominique Orban

Back## Publications

### Cahiers du GERAD

**Dominique Orban**, and Michael A. Saunders

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

BibTeX reference**Dominique Orban**

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...

BibTeX referenceCorrigendum: A proximal quasi-Newton trust-region method for nonsmooth regularized optimization

**Dominique Orban**

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...

BibTeX reference**Dominique Orban**

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...

An interior-point trust-region method for nonsmooth regularized bound-constrained optimization

**Dominique Orban**

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

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

BibTeX referencePLSR1: A limited-memory partitioned quasi-Newton optimizer for partially-separable loss functions

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

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

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We introduce an iterative solver named MINARES for symmetric linear systems `\(Ax \approx b\)`

, where `\(A\)`

is possibly singular.
MINARES is based on t...

The indefinite proximal gradient method

**Dominique Orban**

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. ...

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

BibTeX reference**Dominique Orban**

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...

**Dominique Orban**

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...

**Dominique Orban**, and Abel Soares Siquiera

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

BibTeX referenceOn GSOR, the generalized successive overrelaxation method for double saddle-point problems

**Dominique Orban**, and Michael A. Saunders

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

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

BibTeX reference**Dominique Orban**, and Michael A. Saunders

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

BibTeX referenceComputing a sparse projection into a box

**Dominique Orban**

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....

DCISolver.jl: A Julia solver for nonlinear optimization using dynamic control of infeasibility

**Dominique Orban**, and Abel Soares Siquiera

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

BibTeX reference**Dominique Orban**

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

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

BibTeX reference**Dominique Orban**

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

BibTeX reference**Dominique Orban**, and Michael A. Saunders

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

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RipQP: A multi-precision regularized predictor-corrector method for convex quadratic optimization

**Dominique Orban**

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

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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...

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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)...

BibTeX reference**Dominique Orban**

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

BibTeX reference**Dominique Orban**, and Michael A. Saunders

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

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

BibTeX reference**Dominique Orban**

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 ...

BibTeX reference**Dominique Orban**

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

BibTeX reference**Dominique Orban**, and Michael A. Saunders

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

BibTeX reference**Dominique Orban**

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...

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

BibTeX reference**Dominique Orban**and Abel Soares Siquiera

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

BibTeX referenceImplementing a smooth exact penalty function for equality-constrained nonlinear optimization

**Dominique Orban**, and Michael A. Saunders

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

BibTeX reference**Dominique Orban**, and Michael A. Saunders

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...

**Dominique Orban**

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

BibTeX reference**Dominique Orban**

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

BibTeX referenceStabilized optimization via an NCL algorithm

**Dominique Orban**, and Michael A. Saunders

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

BibTeX reference**Dominique Orban**, Caroline Sainvitu, and Annick Sartenaer

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

BibTeX reference**Dominique Orban**

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

BibTeX referenceNumerical methods for stochastic dynamic programming with application to hydropower optimization

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

BibTeX reference**Dominique Orban**, and Michael A. Saunders

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...

**Dominique Orban**, and Michael A. Saunders

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

BibTeX reference**Dominique Orban**, and Nikolaj van Omme

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

A collection of linear systems arising from interior-point methods for quadratic optimization

**Dominique Orban**

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

BibTeX reference**Dominique Orban**

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

BibTeX reference**Dominique Orban**

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

BibTeX reference**Dominique Orban**

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

BibTeX reference**Dominique Orban**

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...

BibTeX reference**Dominique Orban**

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

BibTeX reference**Dominique Orban**, and Philippe Toint

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

BibTeX reference**Dominique Orban**, and Tyrone Rees

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

BibTeX reference**Dominique Orban**

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

BibTeX reference**Dominique Orban**

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...

BibTeX referenceOptimization of Algorithms with OPAL

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...

BibTeX reference**Dominique Orban**

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

BibTeX reference**Dominique Orban**

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

BibTeX reference**Dominique Orban**, and DP Robinson

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

BibTeX reference**Dominique Orban**

We propose an interior-point algorithm based on an elastic formulation of the `\(\ell_1\)`

-penalty merit function for mathematical programs with complementar...

**Dominique Orban**

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

BibTeX reference**Dominique Orban**

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

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

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

BibTeX reference**Dominique Orban**, and Philippe Toint

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

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

BibTeX reference**Dominique Orban**

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

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

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

BibTeX reference**Dominique Orban**

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...

BibTeX reference**Dominique Orban**, and Philippe Toint

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

BibTeX referenceConvexity and Concavity Detection in Computational Graphs. Tree Walks for Convexity Proving

**Dominique Orban**, and Hermann Schichl

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

BibTeX reference**Dominique Orban**

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

BibTeX referenceDrAmpl - A meta solver for optimization

**Dominique Orban**

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 [...

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

BibTeX reference**Dominique Orban**

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

BibTeX reference**Dominique Orban**, Annick Sartenaer, and Philippe Toint

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...

BibTeX reference**Dominique Orban**, and Philippe Toint

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

BibTeX reference### Articles

**Dominique Orban**, and Michael A. Saunders

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**, and Abel Soares Siquiera

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**and Abel Soares Siquiera

**Dominique Orban**, and Michael A. Saunders

**Dominique Orban**, and Michael A. Saunders

**Dominique Orban**

**Dominique Orban**, Daniel Ruiz, and David Titley-Peloquin

**Dominique Orban**, and Michael A. Saunders

**Dominique Orban**

**Dominique Orban**, and Michael A. Saunders

**Dominique Orban**, and Michael A. Saunders

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**, and Philippe Toint

**Dominique Orban**, and Tyrone Rees

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**, and Kien-Cong Dang

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**, and DP Robinson

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**, and Hermann Schichl

**Dominique Orban**, and Vincent Zalzal

**Dominique Orban**

**Dominique Orban**

**Dominique Orban**, and R. Waltz

**Dominique Orban**, Annick Sartenaer, and Philippe Toint

**Dominique Orban**

**Dominique Orban**, and Philippe Toint

**Dominique Orban**, and Philippe Toint

### Books

### Book chapters

**Dominique Orban**, and Philippe Toint

**Dominique Orban**

**Dominique Orban**

### Proceedings

**Dominique Orban**

**Dominique Orban**, and Andrea Lodi

**Dominique Orban**, and Michael A. Saunders

**Dominique Orban**