Class NelderMead

java.lang.Object

com.quantfinlib.optimization.NelderMead

public final class NelderMead
extends Object

Derivative-free minimisation by the Nelder-Mead simplex method with the standard coefficients (reflection 1, expansion 2, contraction 1/2, shrink 1/2), following Lagarias, Reeds, Wright and Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions", SIAM J. Optim. 9 (1998) 112-147.

Nelder-Mead can stall on a non-stationary point, so minimize(ToDoubleFunction, double[], double, double, int) restarts from the best vertex with a fresh simplex until a restart no longer improves the objective by more than the tolerance. It is meant for smooth problems in a handful of unconstrained variables (likelihoods after a reparameterisation that maps the admissible region onto R^k). An objective value of NaN or +Infinity is treated as "worse than any finite value", which lets the objective reject inadmissible points.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	NelderMead.Result	Result: argmin, minimum, objective evaluations used.

Method Summary

Modifier and Type	Method	Description
static NelderMead.Result	minimize(ToDoubleFunction<double[]> f, double[] start, double step, double tol, int maxEvals)	Minimises f from start.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

minimize

public static NelderMead.Result minimize(ToDoubleFunction<double[]> f,
 double[] start,
 double step,
 double tol,
 int maxEvals)

Minimises f from start.

Parameters:

f - objective; NaN or +Infinity marks an inadmissible point

start - starting point (length k ≥ 1), must give a finite value

step - initial simplex edge in every coordinate, > 0

tol - convergence tolerance on the spread of simplex values, relative to 1 + |f|, and on the restart gain

maxEvals - evaluation budget

Throws:

IllegalArgumentException - if f(start) is not finite

IllegalStateException - if the budget runs out before convergence