TAOBRGN#
Bounded Regularized Gauss-Newton method for solving nonlinear least-squares problems with bound constraints. This algorithm is a thin wrapper around TAOBNTL that constructs the Gauss-Newton problem with the user-provided least-squares residual and Jacobian. The algorithm offers an L2-norm (l2pure), L2-norm proximal point (l2prox) regularizer, and L1-norm dictionary regularizer (l1dict), where we approximate the L1-norm \(\|x\|_1\) by \(\sum_i{\sqrt{x_i^2+\epsilon^2}-\epsilon}\) with a small positive number \(\epsilon\). Also offered is the lm regularizer which uses a scaled diagonal of \(J^T J\). With the lm regularizer, TAOBRGN is a Levenberg-Marquardt optimizer. The user can also provide their own regularization function.
Options Database Keys#
-tao_brgn_regularization_type (user|l2prox|l2pure|l1dict|lm) - regularization type, default
l2prox-tao_brgn_regularizer_weight - regularizer weight (default 1e-4)
-tao_brgn_l1_smooth_epsilon - L1-norm smooth approximation parameter: \(\|x\|_1 = \sum_i{\sqrt{x_i^2+\epsilon^2}-\epsilon}\) (default 1e-6)
See Also#
Tao, TaoBRGNGetSubsolver(), TaoBRGNSetRegularizerWeight(), TaoBRGNSetL1SmoothEpsilon(), TaoBRGNSetDictionaryMatrix(),
TaoBRGNSetRegularizerObjectiveAndGradientRoutine(), TaoBRGNSetRegularizerHessianRoutine()
Level#
beginner
Location#
Examples#
src/tao/leastsquares/tutorials/tomography.c
src/tao/leastsquares/tutorials/cs1.c
Index of all Tao routines
Table of Contents for all manual pages
Index of all manual pages