A curvilinear search using tridiagonal secant updates for unconstrained optimization

dc.creatorDennis Jr., J.E.
dc.creatorEchebest, Nélida Ester
dc.creatorGuardarucci, María Teresa
dc.creatorMartínez, J. M.
dc.creatorScolnik, Hugo Daniel
dc.creatorVacchino, María Cristina
dc.date1991
dc.date2023-03-06T14:12:04Z
dc.date.accessioned2023-07-15T09:44:46Z
dc.date.available2023-07-15T09:44:46Z
dc.identifierhttp://sedici.unlp.edu.ar/handle/10915/149690
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/7489235
dc.descriptionThe idea of doing a curvilinear search along the Levenberg- Marquardt path s(μ) = - (H + μI)⁻¹g always has been appealing, but the cost of solving a linear system for each trial value of the parameter y has discouraged its implementation. In this paper, an algorithm for searching along a path which includes s(μ) is studied. The algorithm uses a special inexpensive QTcQT to QT₊QT Hessian update which trivializes the linear algebra required to compute s(μ). This update is based on earlier work of Dennis-Marwil and Martinez on least-change secant updates of matrix factors. The new algorithm is shown to be local and q-superlinearily convergent to stationary points, and to be globally q-superlinearily convergent for quasi-convex functions. Computational tests are given that show the new algorithm to be robust and efficient.
dc.descriptionFacultad de Ciencias Exactas
dc.formatapplication/pdf
dc.languageen
dc.rightshttp://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rightsCreative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.subjectMatemática
dc.subjectUnconstrained optimization
dc.subjectTrust regions
dc.subjectCurvilinear search
dc.subjectLevenberg-Marquardt
dc.subjectFactor updating
dc.subjectLeast change secant methods
dc.titleA curvilinear search using tridiagonal secant updates for unconstrained optimization
dc.typeArticulo
dc.typePreprint


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