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KrisLibrary
1.0.0
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An iterative solution to minimize f over multidimensional x. May only find a local minimum, depending on the initial point. More...
#include <Minimization.h>
Public Member Functions | |
| MinimizationProblem (ScalarFieldFunction *f) | |
| ConvergenceResult | SolveGD (Real alpha, int &maxIters) |
| Gradient descent. | |
| void | StepGD (Real alpha) |
| ConvergenceResult | SolveSD (int &maxIters) |
| Steepest descent. | |
| ConvergenceResult | SolveCG (int &maxIters) |
| Conjugate gradient. | |
| ConvergenceResult | SolveNewton (int &maxIters) |
| Newton iteration. | |
| ConvergenceResult | SolveQuasiNewton_Ident (int &maxIters) |
| ConvergenceResult | SolveQuasiNewton_Diff (Real dx, int &maxIters) |
| Finite-difference hessian with difference dx. | |
| ConvergenceResult | SolveQuasiNewton (int &maxIters) |
| Hessian given in H. | |
| ConvergenceResult | SolveLM (int &maxIters, Real lambda0=1, Real lambdaScale=10) |
| Levenberg-Marquardt iteration. | |
| ConvergenceResult | LineMinimizationStep (const Vector &dx, Real &alpha0) |
Public Attributes | |
| ScalarFieldFunction * | f |
| Vector | x |
| Real | tolx |
| Real | tolf |
| Real | tolgrad |
| int | verbose |
| std::vector< Vector > * | S |
| Real | fx |
| Vector | grad |
| Vector | dx |
| Matrix | H |
An iterative solution to minimize f over multidimensional x. May only find a local minimum, depending on the initial point.
Optionally, can include bound constraints
Methods:
Gradient descent (GD): move by alpha*gradient.
Steepest descent (SD): alpha*gradient.
Conjugate gradient (CG): use the CG method (Fletcher-Reeves-Polak-Ribiere)
Newton iteraton (Newton): use Newton's method (requires Hessians) Quasi-Newton iteraton (QuasiNewton): use a quasi-Newton method (requires Gradient) Levenberg-marquardt (LM): use Levenberg-marquardt method with starting lambda and lambda update scale factor (requires Hessian) Levenberg-marquardt (LMTrust): same as above, but uses a trust region search
Each method starts at the initial point x. It then determines a direction d and a step size alpha that f(x+alpha*d)<f(x). It then moves x to this position and iterates until maxIters is reached, or one of the 3 termination criteria is met:
change in x < tolx
change in f < tolf
||gradient|| < tolgrad.
The appropriate ConvergenceResult is returned (tolf and tolgrad both return ConvergenceF). tolx is by default 1e-6, tolf is 1e-5, and tolgrad is 1e-8
maxIters is returned as the number of iterations taken.
If S is not NULL it logs the sequence of iterates x0...xn, starting from x1.
| ConvergenceResult MinimizationProblem::LineMinimizationStep | ( | const Vector & | dx, |
| Real & | alpha0 | ||
| ) |
Performs a line search to minimize f(x) in the direction dx. fx must be set to the initial f(x). f is updated to the final x fx is set to the final f(x). Alpha0 is given as the initial step size and returned as the final step size.
Returns the convergence result for the given tolerances or MaxItersReached to continue.
| ConvergenceResult MinimizationProblem::SolveQuasiNewton_Ident | ( | int & | maxIters | ) |
Quasi-newton iteration, with differing initial hessian methods. Identity hessian
1.8.11