Dominique Orban

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

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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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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...

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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...

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

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

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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)...

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

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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...

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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 ...

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

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

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

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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...

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

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

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