Simplex Class Reference

Multi-dimensional simplex class. More...

#include <ql/math/optimization/simplex.hpp>

Inheritance diagram for Simplex:

Collaboration diagram for Simplex:

Public Member Functions
	Simplex (Real lambda)
EndCriteria::Type	minimize (Problem &P, const EndCriteria &endCriteria) override
	minimize the optimization problem P More...
Real	lambda () const
Public Member Functions inherited from OptimizationMethod
virtual	~OptimizationMethod ()=default
virtual EndCriteria::Type	minimize (Problem &P, const EndCriteria &endCriteria)=0
	minimize the optimization problem P More...

Private Member Functions
Real	extrapolate (Problem &P, Size iHighest, Real &factor) const

Private Attributes
Real	lambda_
std::vector< Array >	vertices_
Array	values_
Array	sum_

Detailed Description

Multi-dimensional simplex class.

This method is rather raw and requires quite a lot of computing resources, but it has the advantage that it does not need any evaluation of the cost function's gradient, and that it is quite easily implemented. First, we choose N+1 starting points, given here by a starting point \( \mathbf{P}_{0} \) and N points such that

\[ \mathbf{P}_{\mathbf{i}}=\mathbf{P}_{0}+\lambda \mathbf{e}_{\mathbf{i}}, \]

where \( \lambda \) is the problem's characteristic length scale). These points will form a geometrical form called simplex. The principle of the downhill simplex method is, at each iteration, to move the worst point (highest cost function value) through the opposite face to a better point. When the simplex seems to be constrained in a valley, it will be contracted downhill, keeping the best point unchanged.

Definition at line 58 of file simplex.hpp.

Constructor & Destructor Documentation

Simplex()

Simplex

(

Real

lambda

)

Constructor taking as input the characteristic length

Definition at line 61 of file simplex.hpp.

Member Function Documentation

minimize()

EndCriteria::Type minimize ( Problem &  P, const EndCriteria &  endCriteria  )

overridevirtual

minimize the optimization problem P

Implements OptimizationMethod.

Definition at line 96 of file simplex.cpp.

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lambda()

Real lambda

(

)

const

Definition at line 63 of file simplex.hpp.

extrapolate()

Real extrapolate ( Problem &  P, Size  iHighest, Real &  factor  ) const

private

Definition at line 58 of file simplex.cpp.

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Member Data Documentation

lambda_

Real lambda_

private

Definition at line 69 of file simplex.hpp.

vertices_

std::vector<Array> vertices_

mutableprivate

Definition at line 70 of file simplex.hpp.

values_

Array values_

mutableprivate

Definition at line 71 of file simplex.hpp.

sum_

Array sum_

private

Definition at line 71 of file simplex.hpp.