Lmi0Oracle< Arr036, Mat > Class Template Reference

Oracle for Linear Matrix Inequality (LMI) feasibility problems. More...

#include <lmi0_oracle.hpp>

Inheritance diagram for Lmi0Oracle< Arr036, Mat >:

Collaboration diagram for Lmi0Oracle< Arr036, Mat >:

Public Member Functions
	Lmi0Oracle (size_t ndim, const std::vector< Mat > &F)
	Construct a new LMI Oracle object.
auto	assess_feas (const Arr036 &x) -> Cut *
	Assess the feasibility of a given point.
auto	operator() (const Arr036 &x) -> Cut *
	Call operator wrapping assess_feas.

Public Attributes
LDLTMgr	_mq
	LDLT manager for matrix factorization.

Additional Inherited Members
Protected Types inherited from LmiOracleBase< Arr036, Mat >
using	Cut = std::pair< Arr036, double >
Protected Member Functions inherited from LmiOracleBase< Arr036, Mat >
template<typename LDLT , typename Fn >
auto	assess_impl (LDLT &mgr, const std::vector< Mat > &F, const int sign, const Arr036 &x, Fn &&getA) -> Cut *
	Shared assess_feas skeleton: factor, witness, sym_quad, pack cut.
Protected Attributes inherited from LmiOracleBase< Arr036, Mat >
std::unique_ptr< Cut >	cut = std::make_unique<Cut>()
	Storage for the cut returned by assess_feas.

Detailed Description

template<typename Arr036, typename Mat = Arr036>
class Lmi0Oracle< Arr036, Mat >

Oracle for Linear Matrix Inequality (LMI) feasibility problems.

This oracle solves the following feasibility problem:

find  x
s.t.  F₀ + F₁x₁ + F₂x₂ + ... + Fₙxₙ ⪯ 0

where Fᵢ are symmetric matrices and ⪯ denotes negative semidefinite. This is a fundamental problem in semidefinite programming and control theory.

Note

Concrete oracle in the Template Method pattern: supplies a lazy getA accessor (Σ F_k x_k) with a negative sym_quad sign to the shared LmiOracleBase::assess_impl skeleton.

Template Parameters

Arr036	Array type for the decision variables (size 3-6)
Mat	Matrix type (defaults to Arr036)

Constructor & Destructor Documentation

Lmi0Oracle()

template<typename Arr036 , typename Mat = Arr036>

Lmi0Oracle< Arr036, Mat >::Lmi0Oracle ( size_t  ndim, const std::vector< Mat > &  F  )

inline

Construct a new LMI Oracle object.

Parameters

[in]	ndim	Dimension of the decision space
[in]	F	Vector of matrices defining the LMI constraints

Member Function Documentation

assess_feas()

template<typename Arr036 , typename Mat = Arr036>

auto Lmi0Oracle< Arr036, Mat >::assess_feas ( const Arr036 &  x ) -> Cut*

inline

Assess the feasibility of a given point.

This method checks if the given point x satisfies the LMI constraint. If not feasible, it returns a cutting plane that separates x from the feasible region.

Parameters

[in]

x

The point to assess feasibility

Returns

Pointer to cut information, or nullptr if feasible

operator()()

template<typename Arr036 , typename Mat = Arr036>

auto Lmi0Oracle< Arr036, Mat >::operator() ( const Arr036 &  x ) -> Cut*

inline

Call operator wrapping assess_feas.

Parameters

[in]

x

The point to assess feasibility

Returns

Cut* Pointer to cut, or nullptr if feasible

Member Data Documentation

_mq

template<typename Arr036 , typename Mat = Arr036>

LDLTMgr Lmi0Oracle< Arr036, Mat >::_mq

LDLT manager for matrix factorization.

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

• ellalgo/oracles/lmi0_oracle.hpp