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
882 region with a line search (NTL). They are available via the TAO solvers
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
1710 trust region (BNTR), and trust region with a projected line search
1750 method. Trust-region conjugate gradient methods (`KSPNASH`,
1793 trust-region conjugate gradient method is used for the Hessian
1801 BNTR globalizes the Newton step using a trust region method based on the
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
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