LMIProblem< Arr036, Mat > Class Template Reference

LMI feasibility problem facade. More...

#include <lmi_problem.hpp>

Public Member Functions
	LMIProblem (size_t ndim, std::vector< Mat > F, Mat B)
	Construct a new LMIProblem object.
auto	solve_feas (const Vec &radii, Arr036 xc, const Options &options=Options()) -> std::tuple< Arr036, size_t >
	Solve the LMI feasibility problem.
auto	solve_feas (double alpha, Arr036 xc, const Options &options=Options()) -> std::tuple< Arr036, size_t >
	Solve the LMI feasibility problem (alpha-scaled initial space).

Detailed Description

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

LMI feasibility problem facade.

Owns the LMI data (F matrices and constant term B) and the lazily-created LmiOracle, then drives the cutting-plane method through the standard cutting_plane_feas driver. Hides the 3-step recipe (build oracle -> build search space -> call driver) behind a single call.

The LMI feasibility problem is:

find  x
s.t.  (B - F * x) >= 0   (i.e. B - Σ F_k x_k is positive semidefinite)

Template Parameters

Arr036	Array type for the decision variables
Mat	Matrix type (defaults to Arr036)

Constructor & Destructor Documentation

LMIProblem()

template<typename Arr036 , typename Mat = Arr036>

LMIProblem< Arr036, Mat >::LMIProblem ( size_t  ndim, std::vector< Mat >  F, Mat  B  )

inline

Construct a new LMIProblem object.

Parameters

[in]	ndim	Dimension of the decision space
[in]	F	Vector of matrices F_i (moved in)
[in]	B	Constant term (moved in)

Member Function Documentation

solve_feas() [1/2]

template<typename Arr036 , typename Mat = Arr036>

auto LMIProblem< Arr036, Mat >::solve_feas ( const Vec &  radii, Arr036  xc, const Options &  options = Options()  ) -> std::tuple<Arr036, size_t>

inline

Solve the LMI feasibility problem.

Builds an EllStable search space with the given per-axis radii and initial center, then runs the cutting-plane feasibility method.

Parameters

[in]	radii	Per-axis radii of the initial ellipsoid
[in]	xc	Initial center point (moved in)
[in]	options	Maximum iteration and error tolerance etc.

Returns

Tuple (solution x, number of iterations)

solve_feas() [2/2]

template<typename Arr036 , typename Mat = Arr036>

auto LMIProblem< Arr036, Mat >::solve_feas ( double  alpha, Arr036  xc, const Options &  options = Options()  ) -> std::tuple<Arr036, size_t>

inline

Solve the LMI feasibility problem (alpha-scaled initial space).

Parameters

[in]	alpha	Scaling factor for the initial ellipsoid
[in]	xc	Initial center point (moved in)
[in]	options	Maximum iteration and error tolerance etc.

Returns

Tuple (solution x, number of iterations)

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

• ellalgo/lmi_problem.hpp