forward decl for nonneg orthant cone More...

#include <rplus.hpp>

Inheritance diagram for conic::NonnegOrthantCone< Slack >:

Public Types
using	ConeBase = Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >
	bring into scope alias from cone base

Public Types inherited from conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >
using	T = linalg::vector_element_t< Slack >
	alias for mat type

using	HessianMat = linalg::Matrix< T, M, M >
	hessian type

Public Member Functions
constexpr Slack	x0_impl () const
	default interior point

constexpr Slack	y0_impl () const
	default dual point

constexpr bool	in_cone_impl (const Slack &x) const
	in interior of K

constexpr bool	in_dual_cone_impl (const Slack &y) const
	in interior of K^*

constexpr T	alpha_max_impl (const Slack &x, const linalg::Vector< T, M > &p) const
	fraction to boundary dK

constexpr T	alpha_max_dual_impl (const Slack &y, const linalg::Vector< T, M > &p) const
	fracto to dK^*

constexpr auto	H_impl (const Slack &x, const Slack &y) const
	hessian

constexpr auto	grad_impl (const Slack &x) const
	grad

constexpr T	nu_impl () const
	barrier parameter

constexpr auto	e_impl () const
	e (jordan identity)

constexpr auto	w_impl (const Slack &x, const Slack &y) const
	w (self-scaled point)

constexpr auto	circ_impl (const Slack &x, const Slack &y) const
	circ

template<typename Scaling >
constexpr auto	scaled_affine_correction_impl (const Slack &x, const Scaling &, const Slack &px, const Slack &py) const
	Componentwise form of the NT-scaled affine correction for R^n_+.

constexpr auto	trace_impl (const Slack &x, const Slack &y) const
	trace

constexpr auto	inv_impl (const Slack &x) const
	jordan inverse

constexpr auto	gamma_F_impl (const Slack &x, const Slack &y) const
	gamma_F

Public Member Functions inherited from conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >
constexpr Slack	x0 () const
	default interior point (initial slack in cone space)

constexpr Slack	y0 () const
	default interior point (initial slack in dual cone)

constexpr bool	in_cone (const Slack &x) const
	in the interior of k

constexpr bool	in_dual_cone (const Slack &y) const
	in the interior of K^*

constexpr auto	H (const Slack &x, const Slack &y) const
	hessian

constexpr T	alpha_max (const Slack &x, const linalg::Vector< T, M > &p) const
	fraction to boundary dk

constexpr T	alpha_max_dual (const Slack &y, const linalg::Vector< T, M > &p) const
	fraction to boundary dk^*

constexpr T	nu () const
	barrier parameter

constexpr auto	grad (const Slack &x) const
	gradient

constexpr auto	e () const
	e (jordan identity)

constexpr auto	w (const Slack &x, const Slack &y) const
	w (self-scaling point)

constexpr auto	circ (const Slack &x, const Slack &y) const
	circ (jordan map/product operator)

constexpr auto	trace (const Slack &x, const Slack &y) const
	trace

constexpr auto	inv (const Slack &x) const
	inv (jordan inverse element)

constexpr T	trace_weight () const
	Convert Euclidean complementarity to this cone's Jordan trace units.

constexpr auto	scaled_affine_correction (const Slack &x, const Scaling &P, const Slack &px, const Slack &py) const
	Affine second-order correction in dual coordinates under NT scaling.

constexpr auto	scaled_affine_correction_impl (const Slack &x, const Scaling &P, const Slack &px, const Slack &py) const
	Common symmetric-cone implementation using Jordan operations.

constexpr auto	gamma_F (const Slack &x, const Slack &y) const
	gamma_F (functional proximity neighborhood metric)

constexpr auto	self () const
	self function which returns a const ref to the derived object

Additional Inherited Members
Static Public Attributes inherited from conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >
static constexpr std::size_t	M
	helpers to get M slack size

static constexpr T	eps
	eps constant

Detailed Description

template<linalg::VectorContainer Slack>
struct conic::NonnegOrthantCone< Slack >

forward decl for nonneg orthant cone

nonneg cone class

R^n_+ = set of all nonneg R

Definition at line 46 of file rplus.hpp.

Member Typedef Documentation

◆ ConeBase

template<linalg::VectorContainer Slack>

using conic::NonnegOrthantCone< Slack >::ConeBase = Cone<Slack, NonnegOrthantCone<Slack>, ConeType::SYMMETRIC>

bring into scope alias from cone base

Definition at line 49 of file rplus.hpp.

Member Function Documentation

◆ alpha_max_dual_impl()

template<linalg::VectorContainer Slack>

constexpr T conic::NonnegOrthantCone< Slack >::alpha_max_dual_impl	(	const Slack &	y,
		const linalg::Vector< T, M > &	p
	)		const

inlineconstexpr

fracto to dK^*

Parameters

y	in K
p	in E^*

Returns: alpha_max (dual)

Definition at line 135 of file rplus.hpp.

References conic::NonnegOrthantCone< Slack >::alpha_max_impl().

◆ alpha_max_impl()

template<linalg::VectorContainer Slack>

constexpr T conic::NonnegOrthantCone< Slack >::alpha_max_impl	(	const Slack &	x,
		const linalg::Vector< T, M > &	p
	)		const

inlineconstexpr

fraction to boundary dK

sigma_x = frac{1}{sup{alpha | x + alpha p in K}} sup{alpha | x + alpha p in K} -> -inf(x + alpha p) x + alpha p = 0 -> alpha = -x / p alpha = min. -x_i / p_i

(similar for dual)

Parameters

x	in K or K^*
p	in E or E^* (delta dir)

Returns: alpha_max

Definition at line 114 of file rplus.hpp.

References conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::M.

Referenced by conic::NonnegOrthantCone< Slack >::alpha_max_dual_impl().

◆ circ_impl()

template<linalg::VectorContainer Slack>

constexpr auto conic::NonnegOrthantCone< Slack >::circ_impl	(	const Slack &	x,
		const Slack &	y
	)		const

inlineconstexpr

circ

x circ y

Parameters

x	in K
y	in K^*

Returns: x circ y

Definition at line 250 of file rplus.hpp.

Referenced by conic::NonnegOrthantCone< Slack >::trace_impl().

◆ e_impl()

template<linalg::VectorContainer Slack>

constexpr auto conic::NonnegOrthantCone< Slack >::e_impl ( ) const

inlineconstexpr

e (jordan identity)

e = (1,1,...1)

Returns: e (vector)

Definition at line 213 of file rplus.hpp.

Referenced by conic::NonnegOrthantCone< Slack >::H_impl().

◆ gamma_F_impl()

template<linalg::VectorContainer Slack>

constexpr auto conic::NonnegOrthantCone< Slack >::gamma_F_impl	(	const Slack &	x,
		const Slack &	y
	)		const

inlineconstexpr

gamma_F

Parameters

x	in K
y	in K^*

Returns: gamma_F

Definition at line 325 of file rplus.hpp.

References conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::eps, conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::M, and conic::NonnegOrthantCone< Slack >::nu_impl().

◆ grad_impl()

template<linalg::VectorContainer Slack>

constexpr auto conic::NonnegOrthantCone< Slack >::grad_impl ( const Slack & x ) const

inlineconstexpr

grad

F'(x) = -(1/x)^{T}

Parameters

x	in K or y in K^*

Returns: (F'(x), event)

Definition at line 186 of file rplus.hpp.

References conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::eps, and conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::M.

◆ H_impl()

template<linalg::VectorContainer Slack>

constexpr auto conic::NonnegOrthantCone< Slack >::H_impl	(	const Slack &	x,
		const Slack &	y
	)		const

inlineconstexpr

hessian

F''(w) -> pushforward operator that maps primal / tangent dir to change in gradient at scaling point w... acts as forward sensitivity & curvature

w_i = sqrt(x_i/y_i) F(w) = -log(sum(w_i)) F'(w) = -(1/w)^{T} F''(w) = diag(1/w^2)

Parameters

x	in K
y	in K^*

Returns: (H, event)

Definition at line 156 of file rplus.hpp.

References conic::NonnegOrthantCone< Slack >::e_impl(), conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::eps, conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::M, conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::w(), and conic::NonnegOrthantCone< Slack >::w_impl().

◆ in_cone_impl()

template<linalg::VectorContainer Slack>

constexpr bool conic::NonnegOrthantCone< Slack >::in_cone_impl ( const Slack & x ) const

inlineconstexpr

in interior of K

Parameters

x in K

Returns: bool

Definition at line 82 of file rplus.hpp.

References conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::M.

Referenced by conic::NonnegOrthantCone< Slack >::in_dual_cone_impl().

◆ in_dual_cone_impl()

template<linalg::VectorContainer Slack>

constexpr bool conic::NonnegOrthantCone< Slack >::in_dual_cone_impl ( const Slack & y ) const

inlineconstexpr

in interior of K^*

Parameters

y in K^*

Returns: bool

Definition at line 95 of file rplus.hpp.

References conic::NonnegOrthantCone< Slack >::in_cone_impl().

◆ inv_impl()

template<linalg::VectorContainer Slack>

constexpr auto conic::NonnegOrthantCone< Slack >::inv_impl ( const Slack & x ) const

inlineconstexpr

jordan inverse

Parameters

x	in K or y in K^*

Returns: (inv(x), event)

Definition at line 304 of file rplus.hpp.

References conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::eps, and conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::M.

◆ nu_impl()

template<linalg::VectorContainer Slack>

constexpr T conic::NonnegOrthantCone< Slack >::nu_impl ( ) const

inlineconstexpr

barrier parameter

Returns: nu

Definition at line 204 of file rplus.hpp.

References conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::M.

Referenced by conic::NonnegOrthantCone< Slack >::gamma_F_impl().

◆ scaled_affine_correction_impl()

template<linalg::VectorContainer Slack>

template<typename Scaling >

constexpr auto conic::NonnegOrthantCone< Slack >::scaled_affine_correction_impl	(	const Slack &	x,
		const Scaling &	,
		const Slack &	px,
		const Slack &	py
	)		const

inlineconstexpr

Componentwise form of the NT-scaled affine correction for R^n_+.

Here x circ y is componentwise multiplication. Complementarity gives y_i*dx_i + x_i*dy_i = mu - x_i*y_i - px_i*py_i. Dividing by x_i gives dy_i = -(y_i/x_i)*dx_i - [y_i - mu/x_i + px_i*py_i/x_i]. Thus the reduced dual residual needs px_i*py_i/x_i, not the raw product. The existing interior safeguard bounds the denominator away from zero.

Definition at line 265 of file rplus.hpp.

References conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::eps, and conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::M.

◆ trace_impl()

template<linalg::VectorContainer Slack>

constexpr auto conic::NonnegOrthantCone< Slack >::trace_impl	(	const Slack &	x,
		const Slack &	y
	)		const

inlineconstexpr

trace

trace(x circ y) = sum(x_i y_i)

Parameters

x	in K
y	in K^*

Returns: x circ y

Definition at line 290 of file rplus.hpp.

References conic::NonnegOrthantCone< Slack >::circ_impl(), and conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::M.

◆ w_impl()

template<linalg::VectorContainer Slack>

constexpr auto conic::NonnegOrthantCone< Slack >::w_impl	(	const Slack &	x,
		const Slack &	y
	)		const

inlineconstexpr

w (self-scaled point)

Parameters

x	in K
y	in K^*

Returns: (w, event)

Definition at line 226 of file rplus.hpp.

References conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::eps, conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::M, and conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::w().

Referenced by conic::NonnegOrthantCone< Slack >::H_impl().

◆ x0_impl()

template<linalg::VectorContainer Slack>

constexpr Slack conic::NonnegOrthantCone< Slack >::x0_impl ( ) const

inlineconstexpr

default interior point

Returns: x0

Definition at line 62 of file rplus.hpp.

References conic::Cone< Slack, NonnegOrthantCone< Slack >, ConeType::SYMMETRIC >::M.

Referenced by conic::NonnegOrthantCone< Slack >::y0_impl().

◆ y0_impl()

template<linalg::VectorContainer Slack>

constexpr Slack conic::NonnegOrthantCone< Slack >::y0_impl ( ) const

inlineconstexpr

default dual point

Returns: y0

Definition at line 73 of file rplus.hpp.

References conic::NonnegOrthantCone< Slack >::x0_impl().

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

include/akreon/convex/cone_traits.hpp
include/akreon/convex/cones/rplus.hpp

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ ConeBase

Member Function Documentation

◆ alpha_max_dual_impl()

◆ alpha_max_impl()

◆ circ_impl()

◆ e_impl()

◆ gamma_F_impl()

◆ grad_impl()

◆ H_impl()

◆ in_cone_impl()

◆ in_dual_cone_impl()

◆ inv_impl()

◆ nu_impl()

◆ scaled_affine_correction_impl()

◆ trace_impl()

◆ w_impl()

◆ x0_impl()

◆ y0_impl()