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
TypeCommunication / Conférence
Conference titleInverse Problems, Design and Optimization (IPDO-2004) Symposium
Conference cityRio de Janeiro
Journal nameInverse Problems in Science and Engineering
MetadataShow full item record
Abstract (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 / KeywordsOptimization; Nonlinear least squares; Line search; Curvature step\-sizes
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