Global line search strategies for nonlinear least squares problems based on curvature and projected curvature
Al Khoury, Philippe; Chavent, Guy (2006), Global line search strategies for nonlinear least squares problems based on curvature and projected curvature, Inverse Problems, Design and Optimization (IPDO-2004) Symposium, 2006-03, Rio de Janeiro, Brésil
Type
Communication / ConférenceDate
2006Conference title
Inverse Problems, Design and Optimization (IPDO-2004) SymposiumConference date
2006-03Conference city
Rio de JaneiroConference country
BrésilJournal name
Inverse Problems in Science and EngineeringVolume
14Number
5Publisher
Taylor & Francis
Pages
495-509
Publication identifier
Metadata
Show full item recordAbstract (EN)
In this article, we introduce global line search strategies based on the maximum projected curvature step (MPCS). This step is developed from the maximum curvature step (MCS), defined in [Chavent, G., 2004, Curvature steps and geodesic moves for nonlinear least squares descent algorithms. Inverse Problems in Science and Engineering.] and [Chavent, G., 2002, Curvature steps and geodesic moves for nonlinear least squares descent algorithms, INRIA Report.]. At a point in a descent curve, we introduce the optimization plan, on which we project the acceleration in order to obtain the projected curvature. For a search curve with bounded projected curvature, we compute the lower bound to the arc length of the first stationary point, which defines the MPCS. The convergence of the global strategies based on MPCSs and MCSs is studied for different common descent directions. Preliminary numerical results show that algorithms using the new strategies with steepest descent, Gauss–Newton or Levenberg–Marquardt direction are more efficient than the corresponding ones based on the unit step-size.Subjects / Keywords
Optimization; Nonlinear least squares; Line search; Curvature step\-sizesRelated items
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