arXiv subjects

Harry Oviedo

Publications and source records attributed to Harry Oviedo.

4 recordsLinked to original sources

arXiv2026

The method of ellipcenters with momentum and relaxation for convex quadratic minimization

The method of ellipcenters (ME) is a recent technique developed for unconstrained minimization. Its iteration relies only on first order information and consists of building a suitable two-dimensional ellipse that tries to capture intrinsic ill-conditioning of the problem. The center of the ellipse is taken as the next iterate, which justifies the name of the method. ME was already shown to converge linearly when the objective function is smooth and strongly convex. The special case when the objective is quadratic was studied in the first paper on ME and is also the subject of our work here. In this paper, we propose two variants of ME: RelaxME which adds in ME an additional relaxation step at each iteration and MomME which embeds momentum in ME. We prove linear convergence of RelaxME and MomME and, in particular, we show convergence of RelaxME and MomME (and also of ME) in one iteration when the matrix of the quadratic form has only two distinct eigenvalues. Finally, we provide the results of numerical experiments which compare on five optimization problems (and different combinations of parameters defining these problems) ME, RelaxME, and MomME, with 3 other optimizers: the conjugate gradient method [10], Barzilai and Borwein gradient method with long step [2], and the gradient method with adaptive spectral step length [7]. On most instances, MomME provides the smallest number of iterations and conjugate gradient and MomME provide the smallest CPU times and similar CPU times. This opens optimistic possibilities for ME with momentum in broader settings.

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arXiv2022

Circumcentric directions of cones

Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide inward directions to sets given by convex inequalities. In particular, we show that circumcentric directions of finitely generated cones belong to the interior of their polars. We also derive a measure of interiorness of the circumcentric direction, which then provides a special cone of search directions, all being feasible to the convex region under consideration.

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arXiv2020

Spectral Residual Method for Nonlinear Equations on Riemannian Manifolds

In this paper, the spectral algorithm for nonlinear equations (SANE) is adapted to the problem of finding a zero of a given tangent vector field on a Riemannian manifold. The generalized version of SANE uses, in a systematic way, the tangent vector field as a search direction and a continuous real-valued function that adapts this direction and ensures that it verifies a descent condition for an associated merit function. In order to speed up the convergence of the proposed method, we incorporate a Riemannian adaptive spectral parameter in combination with a non-monotone globalization technique. The global convergence of the proposed procedure is established under some standard assumptions. Numerical results indicate that our algorithm is very effective and efficient solving tangent vector field on different Riemannian manifolds and competes favorably with a Polak-Ribiére-Polyak Method recently published and other methods existing in the literature.

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arXiv2017

A Non-monotone Linear Search Method with Mixed Direction on Stiefel Manifold

In this paper, we propose a non-monotone line search method for solving optimization problems on Stiefel manifold. Our method uses as a search direction a mixed gradient based on a descent direction, and a Barzilai-Borwein line search. Feasibility is guaranteed by projecting each iterate on the Stiefel manifold, through SVD factorizations. Some theoretical results for analyzing the algorithm are presented. Finally, we provide numerical experiments comparing our algorithm with other state-of-the-art procedures.

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