# TAOBNK#

Shared base-type for Bounded Newton-Krylov type algorithms. At each iteration, the BNK methods solve the symmetric system of equations to obtain the step diretion dk: Hk dk = -gk for free variables only. The step can be globalized either through trust-region methods, or a line search, or a heuristic mixture of both.

## Options Database Keys#

maximum number of bounded conjugate-gradient iterations taken in each Newton loop**-tao_bnk_max_cg_its -**trust radius initialization method (“constant”, “direction”, “interpolation”)**-tao_bnk_init_type -**trust radius update method (“step”, “direction”, “interpolation”)**-tao_bnk_update_type -**active-set estimation method (“none”, “bertsekas”)**-tao_bnk_as_type -**(developer) initial tolerance used in estimating bounded active variables (-as_type bertsekas)**-tao_bnk_as_tol -**(developer) trial step length used in estimating bounded active variables (-as_type bertsekas)**-tao_bnk_as_step -**(developer) Hessian perturbation starting value**-tao_bnk_sval -**(developer) minimum initial Hessian perturbation**-tao_bnk_imin -**(developer) maximum initial Hessian perturbation**-tao_bnk_imax -**(developer) minimum Hessian perturbation**-tao_bnk_pmin -**(developer) aximum Hessian perturbation**-tao_bnk_pmax -**(developer) Hessian perturbation growth factor**-tao_bnk_pgfac -**(developer) Hessian perturbation shrink factor**-tao_bnk_psfac -**(developer) initial merit factor for Hessian perturbation**-tao_bnk_imfac -**(developer) merit growth factor for Hessian perturbation**-tao_bnk_pmgfac -**(developer) merit shrink factor for Hessian perturbation**-tao_bnk_pmsfac -**(developer) threshold for rejecting step (-update_type reduction)**-tao_bnk_eta1 -**(developer) threshold for accepting marginal step (-update_type reduction)**-tao_bnk_eta2 -**(developer) threshold for accepting reasonable step (-update_type reduction)**-tao_bnk_eta3 -**(developer) threshold for accepting good step (-update_type reduction)**-tao_bnk_eta4 -**(developer) radius reduction factor for rejected step (-update_type reduction)**-tao_bnk_alpha1 -**(developer) radius reduction factor for marginally accepted bad step (-update_type reduction)**-tao_bnk_alpha2 -**(developer) radius increase factor for reasonable accepted step (-update_type reduction)**-tao_bnk_alpha3 -**(developer) radius increase factor for good accepted step (-update_type reduction)**-tao_bnk_alpha4 -**(developer) radius increase factor for very good accepted step (-update_type reduction)**-tao_bnk_alpha5 -**(developer) tolerance for small pred/actual ratios that trigger automatic step acceptance (-update_type reduction)**-tao_bnk_epsilon -**(developer) threshold for accepting very good step (-update_type interpolation)**-tao_bnk_mu1 -**(developer) threshold for accepting good step (-update_type interpolation)**-tao_bnk_mu2 -**(developer) radius reduction factor for rejected very bad step (-update_type interpolation)**-tao_bnk_gamma1 -**(developer) radius reduction factor for rejected bad step (-update_type interpolation)**-tao_bnk_gamma2 -**(developer) radius increase factor for accepted good step (-update_type interpolation)**-tao_bnk_gamma3 -**(developer) radius increase factor for accepted very good step (-update_type interpolation)**-tao_bnk_gamma4 -**(developer) trust region interpolation factor (-update_type interpolation)**-tao_bnk_theta -**(developer) threshold for small line-search step length (-update_type step)**-tao_bnk_nu1 -**(developer) threshold for reasonable line-search step length (-update_type step)**-tao_bnk_nu2 -**(developer) threshold for large line-search step length (-update_type step)**-tao_bnk_nu3 -**(developer) threshold for very large line-search step length (-update_type step)**-tao_bnk_nu4 -**(developer) radius reduction factor for very small line-search step length (-update_type step)**-tao_bnk_omega1 -**(developer) radius reduction factor for small line-search step length (-update_type step)**-tao_bnk_omega2 -**(developer) radius factor for decent line-search step length (-update_type step)**-tao_bnk_omega3 -**(developer) radius increase factor for large line-search step length (-update_type step)**-tao_bnk_omega4 -**(developer) radius increase factor for very large line-search step length (-update_type step)**-tao_bnk_omega5 -**(developer) threshold for accepting very good step (-init_type interpolation)**-tao_bnk_mu1_i -**(developer) threshold for accepting good step (-init_type interpolation)**-tao_bnk_mu2_i -**(developer) radius reduction factor for rejected very bad step (-init_type interpolation)**-tao_bnk_gamma1_i -**(developer) radius reduction factor for rejected bad step (-init_type interpolation)**-tao_bnk_gamma2_i -**(developer) radius increase factor for accepted good step (-init_type interpolation)**-tao_bnk_gamma3_i -**(developer) radius increase factor for accepted very good step (-init_type interpolation)**-tao_bnk_gamma4_i -**(developer) trust region interpolation factor (-init_type interpolation)**-tao_bnk_theta_i -**

## Level#

beginner

## Location#

Index of all Tao routines

Table of Contents for all manual pages

Index of all manual pages