petsc-master 2015-11-27
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# TAONLS

Newton's method with linesearch for unconstrained minimization. At each iteration, the Newton line search method solves the symmetric system of equations to obtain the step diretion dk: Hk dk = -gk a More-Thuente line search is applied on the direction dk to approximately solve min_t f(xk + t d_k)

### Options Database Keys

 -tao_nls_ksp_type - "cg","nash","stcg","gltr","petsc" -tao_nls_pc_type - "none","ahess","bfgs","petsc" -tao_nls_bfgs_scale_type - "ahess","phess","bfgs" -tao_nls_init_type - "constant","direction","interpolation" -tao_nls_update_type - "step","direction","interpolation" -tao_nls_sval - perturbation starting value -tao_nls_imin - minimum initial perturbation -tao_nls_imax - maximum initial perturbation -tao_nls_pmin - minimum perturbation -tao_nls_pmax - maximum perturbation -tao_nls_pgfac - growth factor -tao_nls_psfac - shrink factor -tao_nls_imfac - initial merit factor -tao_nls_pmgfac - merit growth factor -tao_nls_pmsfac - merit shrink factor -tao_nls_eta1 - poor steplength; reduce radius -tao_nls_eta2 - reasonable steplength; leave radius -tao_nls_eta3 - good steplength; increase readius -tao_nls_eta4 - excellent steplength; greatly increase radius -tao_nls_alpha1 - alpha1 reduction -tao_nls_alpha2 - alpha2 reduction -tao_nls_alpha3 - alpha3 reduction -tao_nls_alpha4 - alpha4 reduction -tao_nls_alpha - alpha5 reduction -tao_nls_mu1 - mu1 interpolation update -tao_nls_mu2 - mu2 interpolation update -tao_nls_gamma1 - gamma1 interpolation update -tao_nls_gamma2 - gamma2 interpolation update -tao_nls_gamma3 - gamma3 interpolation update -tao_nls_gamma4 - gamma4 interpolation update -tao_nls_theta - theta interpolation update -tao_nls_omega1 - omega1 step update -tao_nls_omega2 - omega2 step update -tao_nls_omega3 - omega3 step update -tao_nls_omega4 - omega4 step update -tao_nls_omega5 - omega5 step update -tao_nls_mu1_i - mu1 interpolation init factor -tao_nls_mu2_i - mu2 interpolation init factor -tao_nls_gamma1_i - gamma1 interpolation init factor -tao_nls_gamma2_i - gamma2 interpolation init factor -tao_nls_gamma3_i - gamma3 interpolation init factor -tao_nls_gamma4_i - gamma4 interpolation init factor -tao_nls_theta_i - theta interpolation init factor