:orphan:
# 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_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 radius
- ***-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




## Level
beginner

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/tao/unconstrained/impls/nls/nls.c.html#TAONLS">src/tao/unconstrained/impls/nls/nls.c</A>

## Examples
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/tao/constrained/tutorials/tomographyADMM.c.html">src/tao/constrained/tutorials/tomographyADMM.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/tao/tutorials/ex4.c.html">src/tao/tutorials/ex4.c</A><BR>


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


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