QCQP Class Reference

A Quadratically Constrained Quadratic Program solver class. More...

#include <QCQP.h>

Inheritance diagram for QCQP:

Public Member Functions
IPM_Error	solve (IPM_Vector &x, const IPM_Matrix P[], const IPM_Vector q[], const IPM_Single r[], const IPM_uint m, const IPM_Matrix &A, const IPM_Vector &b)
	Runs the solver with given parameters. More...
bool	isConverged (void)
	Indicates if the previous solve() has converged or not.
Public Member Functions inherited from PrimalDualIPM
	PrimalDualIPM ()
	Constructor.
virtual	~PrimalDualIPM ()
	Destructor.
void	setLog (std::ostream *pOuts)
	Sets output destination of internal calculation log. More...

Protected Attributes
IPM_Scalar	m_slack
	Initial margin value for a slack variable.
Protected Attributes inherited from PrimalDualIPM
IPM_Scalar	m_margin
	Initial margin value for dual variables of inequalities.
IPM_Scalar	m_loop
	Max iteration number of outer-loop for the Newton step.
IPM_Scalar	m_bloop
	Max iteration number of inner-loop for the backtracking line search.
IPM_Scalar	m_eps_feas
	Tolerance of the primal and dual residuals.
IPM_Scalar	m_eps
	Tolerance of the surrogate duality gap.
IPM_Scalar	m_mu
	The factor to squeeze complementary slackness.
IPM_Scalar	m_alpha
	The factor to decrease residuals in the backtracking line search.
IPM_Scalar	m_beta
	The factor to decrease a step size in the backtracking line search.
IPM_Scalar	m_s_coef
	The factor to determine an initial step size in the backtracking line search.

Additional Inherited Members
Protected Member Functions inherited from PrimalDualIPM
void	logWarn (const char *str)
	Logs a warning message. More...
void	logVector (const char *str, IPM_Vector_IN v)
	Logs values of a vector, transposing if it is a colomn vector. More...
void	logMatrix (const char *str, IPM_Matrix_IN m)
	Logs values of a matrix. More...
IPM_Error	start (const IPM_uint n, const IPM_uint m, const IPM_uint p)
	Starts to solve a optimization problem by primal-dual interior-point method. More...
Static Protected Member Functions inherited from PrimalDualIPM
static IPM_Scalar	max (const IPM_Scalar a, const IPM_Scalar b)
	Returns the larger of a and b.
static IPM_Scalar	min (const IPM_Scalar a, const IPM_Scalar b)
	Returns the smaller of a and b.
static IPM_Scalar	abs (const IPM_Scalar x)
	Returns the absolute value of x.

Detailed Description

A Quadratically Constrained Quadratic Program solver class.

The problem is \[ \begin{array}{ll} {\rm minimize} & {1 \over 2} x^T P_0 x + q_0^T x + r_0 \\ {\rm subject \ to} & {1 \over 2} x^T P_i x + q_i^T x + r_i \le 0 \quad (i = 1, \ldots, m) \\ & A x = b, \end{array} \] where

• variables \( x \in {\bf R}^n \)
• \( P_j \in {\bf S}_{+}^n \), \( q_j \in {\bf R}^n \), \( r_j \in {\bf R} \) for \( j = 0, \ldots, m \)
• \( A \in {\bf R}^{p \times n} \), \( b \in {\bf R}^p \).

Internally a slack variable \( s \in {\bf R} \) is introduced for the infeasible start method as follows: \[ \begin{array}{ll} {\rm minimize}_{x,s} & {1 \over 2} x^T P_0 x + q_0^T x + r_0 \\ {\rm subject \ to} & {1 \over 2} x^T P_i x + q_i^T x + r_i \le s \quad (i = 1, \ldots, m) \\ & A x = b \\ & s = 0. \end{array} \]

Member Function Documentation

IPM_Error QCQP::solve	(	IPM_Vector &	x,
		const IPM_Matrix	P[],
		const IPM_Vector	q[],
		const IPM_Single	r[],
		const IPM_uint	m,
		const IPM_Matrix &	A,
		const IPM_Vector &	b
	)

Runs the solver with given parameters.

Parameters

x	[IN-OUT] is a column vector containing values of \(x\). It is used as the initial values and overwritten with the final results.
P	[IN] is an array of matrices containing values of \(P_0, \ldots, P_m\).
q	[IN] is an array of vectors containing values of \(q_0, \ldots, q_m\).
r	[IN] is an array of single element matrices containing values of \(r_0, \ldots, r_m\).
m	is \(m\), the number of inequality constraints.
A	[IN] is a matrix containing values of \(A\).
b	[IN] is a vector containing values of \(b\).

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

• QCQP.h
• QCQP.cpp