# 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
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/tao/unconstrained/impls/ntr/ntr.c.html#TAONTR">src/tao/unconstrained/impls/ntr/ntr.c</A>


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[Edit on GitLab](https://gitlab.com/petsc/petsc/-/edit/release/src/tao/unconstrained/impls/ntr/ntr.c)


[Index of all Tao routines](index.md)  
[Table of Contents for all manual pages](/docs/manualpages/index.md)  
[Index of all manual pages](/docs/manualpages/singleindex.md)  
