PETSc version 3.17.0
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# TAONTR

Newton's method with trust region for unconstrained minimization. At each iteration, the Newton trust region method solves the system. NTR expects a KSP solver with a trust region radius. min_d .5 dT Hk d + gkT d, s.t. ||d|| < Delta_k

### Options Database Keys

| -tao_ntr_init_type | - "constant","direction","interpolation"
| -tao_ntr_update_type | - "reduction","interpolation"
| -tao_ntr_min_radius | - lower bound on trust region radius
| -tao_ntr_max_radius | - upper bound on trust region radius
| -tao_ntr_epsilon | - tolerance for accepting actual / predicted reduction
| -tao_ntr_mu1_i | - mu1 interpolation init factor
| -tao_ntr_mu2_i | - mu2 interpolation init factor
| -tao_ntr_gamma1_i | - gamma1 interpolation init factor
| -tao_ntr_gamma2_i | - gamma2 interpolation init factor
| -tao_ntr_gamma3_i | - gamma3 interpolation init factor
| -tao_ntr_gamma4_i | - gamma4 interpolation init factor
| -tao_ntr_theta_i | - theta1 interpolation init factor
| -tao_ntr_eta1 | - eta1 reduction update factor
| -tao_ntr_eta2 | - eta2 reduction update factor
| -tao_ntr_eta3 | - eta3 reduction update factor
| -tao_ntr_eta4 | - eta4 reduction update factor
| -tao_ntr_alpha1 | - alpha1 reduction update factor
| -tao_ntr_alpha2 | - alpha2 reduction update factor
| -tao_ntr_alpha3 | - alpha3 reduction update factor
| -tao_ntr_alpha4 | - alpha4 reduction update factor
| -tao_ntr_alpha4 | - alpha4 reduction update factor
| -tao_ntr_mu1 | - mu1 interpolation update
| -tao_ntr_mu2 | - mu2 interpolation update
| -tao_ntr_gamma1 | - gamma1 interpolcation update
| -tao_ntr_gamma2 | - gamma2 interpolcation update
| -tao_ntr_gamma3 | - gamma3 interpolcation update
| -tao_ntr_gamma4 | - gamma4 interpolation update
| -tao_ntr_theta | - theta interpolation update

### Level

beginner

### Location

src/tao/unconstrained/impls/ntr/ntr.c
Index of all Tao routines
Table of Contents for all manual pages
Index of all manual pages