José Luis Morales

• PhD
• Professor at National Autonomous University of Mexico

The variational fitting of the Fock potential employing localized molecular orbitals requires either the inversion of the local two-center Coulomb matrices or alternatively the solution of corresponding linear equation systems with these matrices. In both cases, the method of choice is the Cholesky decomposition of the formally positive definite lo...

In this work we present the implementation of a variational density fitting methodology that uses iterative linear algebra for solving the associated system of linear equations. It is well known that most difficulties with this system arise from the fact that the coefficient matrix is in general ill-conditioned and, due to finite precision round-of...

Computation of molecular orbital electron repulsion integrals (MO-ERIs) as a transformation from atomic orbital electron repulsion integrals (AO-ERIs) is the bottleneck of second order electron propagator calculations when a single orbital is studied. In this contribution, asymmetric density fitting is combined with modified Cholesky decomposition...

The features in a clinical history from a patient with suspected primary immunodeficiency (PID) direct the differential diagnosis through pattern recognition. PIDs are a heterogeneous group of more than 250 congenital diseases with increased susceptibility to infection, inflammation, autoimmunity, allergy and malignancy. Linear discriminant analysi...

A sequential quadratic programming (SQP) method is presented that aims to over-come some of the drawbacks of contemporary SQP methods. It avoids the difficulties associated with indefinite quadratic programming subproblems by defining this sub-problem to be always convex. The novel feature of the approach is the addition of an equality constrained...

This remark describes an improvement and a correction to Algorithm 778. It is shown that the performance of the algorithm can be improved significantly by making a relatively simple modification to the subspace minimization phase. The correction concerns an error caused by the use of routine dpmeps to estimate machine precision.

In the Black-Scholes-Merton model, as well as in more general stochastic models in finance, the price of an American option solves a parabolic variational inequality. When the variational inequality is discretized, one obtains a linear complementarity problem that must be solved at each time step. This paper presents an algorithm for the solution o...

In this paper we propose an iterative method for solving the inhomogeneous systems of linear equations associated with density fitting. The proposed method is based on a version of the conjugate gradient method that makes use of automatically built quasi-Newton preconditioners. The paper gives a detailed description of a parallel implementation of...

In this paper we propose the use of new iterative methods to solve symmetric linear complementarity problems (SLCP) that arise in the computation of dry frictional contacts in multi-rigid-body dynamics. Specifically, we explore the two-stage iterative algorithm developed by Morales, Nocedal and Smelyanskiy. The underlying idea of that method is to...

A numerical study of model-based methods for derivative-free optimization is presented. These methods typically include a geometry phase whose goal is to ensure the adequacy of the interpolation set. The paper studies the performance of an algorithm that dispenses with the geometry phase altogether (and therefore does not attempt to control the pos...

This paper studies algorithms for the solution of mixed symmetric linear complementarity problems. The goal is to compute fast and approximate solutions of medium to large sized problems, such as those arising in computer game simulations and American options pricing. The paper proposes an improvement of a method described by Kocvara and Zowe (Nume...

An interior-point method for nonlinear programming is presented. It enjoys the flexibility of switching between a line search method that computes steps by factoring the primal-dual equations and a trust region method that uses a conjugate gradient iteration. Steps computed by direct factorization are always tried first, but if they are deemed inef...

A series of numerical experiments with interior point (LOQO, KNITRO) and active-set sequential quadratic programming (SNOPT, filterSQP) codes are reported and analyzed. The tests were performed with small, medium-size and moderately large problems, and are examined by problem classes. Detailed observations on the performance of the codes, and sever...

The application of quasi-Newton methods is widespread in numerical optimization. Independently of the application, the techniques used to update the BFGS matrices seem to play an important role in the performance of the overall method. In this paper, we address precisely this issue. We compare two implementations of the limited memory BFGS method f...

This paper describes a class of optimization methods that interlace iterations of the limited memory BFGS method (L-BFGS) and a Hessian-free Newton method (HFN) in such a way that the information collected by one type of iteration improves the performance of the other. Curvature information about the objective function is stored in the form of a li...

PREQN is a package of Fortran 77 subroutines for automatically generating preconditioners for the conjugate gradient method. It is designed for solving a sequence of linear systems Aix = bi, i = 1, . . . , t, where the coefficient matrices Ai are symmetric and positive definite and vary slowly. Problems of this type arise, for example, in nonlinear...

This paper proposes a preconditioner for the conjugate gradient method (CG) that is designed for solving systems of equations Acursive Greek chi = bi with different right-hand-side vectors or for solving a sequence of slowly varying systems Akcursive Greek chi = bk. The preconditioner has the form of a limited memory quasi-Newton matrix and is gene...

PREQN is a package of Fortran 77 subroutines for automatically generating preconditioners for the conjugate gradient method. It is designed for solving a sequence of linear systems A i x = b i ; i = 1; : : : ; t, where the coefficient matrices A i are symmetric and positive definite and vary slowly. The preconditioners are based on limited memory q...

In this work we present a truncated Newton method able to deal with large scale bound constrained optimization problems. These problems are p osed during the process of identifying parameters in mathematical models. Speciically, we propose a new termination rule for the inner iteration, that is eeective in this class of applications. Preliminary nu...

The purpose of the note is to facilitate and motivate the introduction and study of quasi-Newton formulas in the classroom. We show how to construct ele-mentary quasi-Newton formulas that satisfy a variational condition. The approach presented makes use of elementary concepts in equality constrained optimization and linear algebra. We start by cons...