doc/manual/tao.md

89 gradient, Newton with line search or trust region) but also can
559 Other stopping criteria include a minimum trust-region radius or a
863    Newton line search (`tao_nls`), Newton trust-region (`tao_ntr`),
864    and Newton trust-region line-search (`tao_ntl`)
869 trust-region methods will likely perform best. When a Hessian evaluation
881 for unconstrained optimization: line search (NLS), trust region (NTR), and trust
1190 of equation, a trust-region radius needs to be initialized and updated.
1191 This trust-region radius simultaneously limits the size of the step
1193 method. The method for initializing the trust-region radius is set with
1203 algorithm. The `constant` method initializes the trust-region radius
1207 standard conjugate gradient method and initializes the trust region to
1210 The method for updating the trust-region radius is set with the command
1212 `step` is the default. The `step` method updates the trust-region
1250 initialization to compute a new value for the trust-region radius.
1258 The Newton trust-region method solves the constrained quadratic
1271 trust-region radius. If $x_k + d_k$ sufficiently reduces the
1273 trust-region radius is updated. However, if $x_k + d_k$ does not
1275 rejected, the trust-region radius is reduced, and the quadratic program
1276 is re-solved by using the updated trust-region radius. The Newton
1277 trust-region method can be set by using the TAO solver `tao_ntr`. The
1468 The method for computing an initial trust-region radius is set with the
1477 function value is used as the starting point for the main trust-region
1478 algorithm. The `constant` method initializes the trust-region radius
1482 standard conjugate gradient method and initializes the trust region to
1485 The method for updating the trust-region radius is set with the command
1508 initialization to compute a new value for the trust-region radius.
1516 NTL safeguards the trust-region globalization such that a line search
1520 scaled gradient or a gradient descent step. The trust radius is then
1710 trust region (BNTR), and trust region with a projected line search
1793 trust-region conjugate gradient method is used for the Hessian
1794 inversion, the trust radius is modified based on the line search step
1801 BNTR globalizes the Newton step using a trust region method based on the
1802 predicted versus actual reduction in the cost function. The trust radius
1803 is increased only if the accepted step is at the trust region boundary.
1812 BNTL safeguards the trust-region globalization such that a line search
1816 scaled gradient or a gradient descent step. The trust radius is then
1843 shifting, or the BNTR framework with trust region safeguards, can
1849 (BQNKLS), trust region (BQNKTR) and trust region w/ line search
2064 trust-region method (TAOBQNKTR). Other first-order methods such as
2065 TAOBNCG and TAOBQNLS are also appropriate, but a trust-region
2448 (`tao_pounders`). POUNDERS employs a derivative-free trust-region
2463 trust-region subproblem
2472 where $\Delta_k$ is the current trust-region radius. By default we
2473 use a trust-region norm with $p=\infty$ and solve
2480 trust region that may interfere with the infinity-norm trust region used
2491 approximation on the trust region is then used to update the iterate,
2503 and trust-region radius,
2520 trust-region radius remain unchanged after the above updates, and the
2572 : The initial trust-region radius ($>0$, real). This is used to
2811 trust region. All the options that apply to TRON except for trust-region
2866 and lower bounds. The TRON algorithm applies a trust region to the
2867 conjugate gradients to ensure convergence. The initial trust-region
2869 `TaoSetInitialTrustRegionRadius()`, and the current trust region size
2871 The initial trust region can significantly alter the rate of convergence