sgpp::optimization::test_problems::TremblingParabolaObjective Class Reference

Trembling parabola objective function. More...

#include <TremblingParabola.hpp>

Inheritance diagram for sgpp::optimization::test_problems::TremblingParabolaObjective:

Public Member Functions
void	clone (std::unique_ptr< ScalarFunction > &clone) const override
double	evalUndisplaced (const base::DataVector &x) override
	TremblingParabolaObjective (size_t d, size_t p)
	Constructor. More...
	~TremblingParabolaObjective () override
	Destructor. More...
Public Member Functions inherited from sgpp::optimization::test_problems::TestScalarFunction
double	eval (const base::DataVector &x) override
	Evaluate displaced function. More...
const base::DataVector &	getDisplacement () const
void	setDisplacement (const base::DataVector &displacement)
	TestScalarFunction (size_t d)
	Constructor. More...
	~TestScalarFunction () override
	Destructor. More...
Public Member Functions inherited from sgpp::optimization::ScalarFunction
size_t	getNumberOfParameters () const
	ScalarFunction (size_t d)
	Constructor. More...
virtual	~ScalarFunction ()
	Destructor. More...

Protected Member Functions
double	splineTrembling (double x) const

Protected Attributes
const base::SBsplineBase	bSplineBasis
const double	g0
const size_t	p
Protected Attributes inherited from sgpp::optimization::test_problems::TestScalarFunction
base::DataVector	displacement
	displacement vector More...
base::DataVector	xTmp
	temporary vector for displacing More...
Protected Attributes inherited from sgpp::optimization::ScalarFunction
size_t	d
	dimension of the domain More...

Detailed Description

Trembling parabola objective function.

Definition:

\[\bar{f}(\bar{\vec{x}}) := \sum_{t=1}^d \left(\bar{x}_t^2/10 + \frac{|\bar{x}_t|}{2} \left(\frac{g^p(\bar{x}_t)}{g^p(0)} + 1\right)\right),\qquad g^p(x) := \sum_{k \sim x} (-1)^k b^p(x - k + (p+1)/2)\]

with \(b^p\) being the B-spline with knots \((0, 1, \dotsc, p + 1)\) (degree \(p\)) and the sum running over all \(k\) for which the summand doesn't vanish

Constructor & Destructor Documentation

TremblingParabolaObjective()

sgpp::optimization::test_problems::TremblingParabolaObjective::TremblingParabolaObjective	(	size_t	d,
		size_t	p
	)

Constructor.

Parameters

d	dimension of the domain
p	smoothness of the function ( \(p\) times continuously differentiable)

Referenced by clone().

~TremblingParabolaObjective()

sgpp::optimization::test_problems::TremblingParabolaObjective::~TremblingParabolaObjective ( )

override

Destructor.

Member Function Documentation

clone()

void sgpp::optimization::test_problems::TremblingParabolaObjective::clone ( std::unique_ptr< ScalarFunction > &  clone ) const

overridevirtual

Parameters

[out]

clone

pointer to cloned object

Implements sgpp::optimization::ScalarFunction.

References TremblingParabolaObjective().

evalUndisplaced()

double sgpp::optimization::test_problems::TremblingParabolaObjective::evalUndisplaced ( const base::DataVector &  x )

overridevirtual

Parameters

x	point \(\vec{x} \in [0, 1]^d\)

Returns

\(f(\vec{x})\)

Implements sgpp::optimization::test_problems::TestScalarFunction.

References sgpp::optimization::ScalarFunction::d, g0, and splineTrembling().

splineTrembling()

double sgpp::optimization::test_problems::TremblingParabolaObjective::splineTrembling ( double  x ) const

inlineprotected

References bSplineBasis, p, and sgpp::base::BsplineBasis< LT, IT >::uniformBSpline().

Referenced by evalUndisplaced().

Member Data Documentation

bSplineBasis

const base::SBsplineBase sgpp::optimization::test_problems::TremblingParabolaObjective::bSplineBasis

protected

Referenced by splineTrembling().

g0

const double sgpp::optimization::test_problems::TremblingParabolaObjective::g0

protected

Referenced by evalUndisplaced().

p

const size_t sgpp::optimization::test_problems::TremblingParabolaObjective::p

protected

Referenced by splineTrembling().

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The documentation for this class was generated from the following files:

• optimization/src/sgpp/optimization/test_problems/unconstrained/TremblingParabola.hpp
• optimization/src/sgpp/optimization/test_problems/unconstrained/TremblingParabola.cpp