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Darwin
1.10(beta)
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Darwin
1.10(beta)
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Public Member Functions | |
| drwnLogBarrierQPSolver () | |
| default constructor | |
| drwnLogBarrierQPSolver (const MatrixXd &P, const VectorXd &q, double r=0.0) | |
| construct an unconstrained QP | |
| virtual bool | findFeasibleStart () |
finds a feasible starting point (or returns false if infeasible) | |
| virtual void | initialize (const VectorXd &x) |
| initialize to feasible point | |
| virtual double | solve () |
| solve the QP and return the objective value | |
 Public Member Functions inherited from drwnQPSolver | |
| drwnQPSolver () | |
| default constructor | |
| drwnQPSolver (const MatrixXd &P, const VectorXd &q, double r=0.0) | |
| construct an unconstrained QP | |
| void | setObjective (const MatrixXd &P, const VectorXd &q, double r=0.0) |
| set the objective function for the QP (dimensions must agree) | |
| void | setEqConstraints (const MatrixXd &A, const VectorXd &b) |
| set the linear equality constraints for the QP (dimensions must agree) | |
| void | setIneqConstraints (const MatrixXd &G, const VectorXd &h) |
| set the linear inequality constraints for the QP (dimensions must agree) | |
| void | setBounds (const VectorXd &lb, const VectorXd &ub) |
| set the upper and lower bounds for each variable, i.e., box constraints | |
| void | clearEqConstraints () |
| clear the linear equality constraints | |
| void | clearIneqConstraints () |
| clear the linear inequality constraints | |
| void | clearBounds () |
| clear the upper and lower bounds on each variable | |
| double | objective () const |
| return the current value of the objective (this is the solution if the solve() function was previously executed and the problem has not changed) | |
| double | objective (const VectorXd &x) const |
| return the objective value for a given feasible point | |
| VectorXd | solution () const |
| return the current estimate of the solution | |
| int | size () const |
| return the number of dimensions of the state space | |
| double | operator[] (unsigned i) const |
access the i-th dimension of the current solution | |
Static Public Attributes | |
| static double | t0 = 5.0 |
| static double | mu = 20.0 |
| Static Public Attributes inherited from drwnQPSolver | |
| static double | alpha = 0.3 |
| line search stopping criterion in (0, 1/2) | |
| static double | beta = 0.5 |
| line search backtracking parameter in (0, 1) | |
Additional Inherited Members | |
| Protected Member Functions inherited from drwnQPSolver | |
| VectorXd | gradient () const |
| VectorXd | gradient (const VectorXd &x) const |
| bool | isFeasiblePoint (const VectorXd &x) const |
| double | solveOnlyBounds () |
| double | solveSingleEquality () |
| double | solveSimplex () |
| double | solveNoBounds () |
| double | solveGeneral () |
| double | lineSearchNoBounds (const VectorXd &x, const VectorXd &dx, const VectorXd &nu, const VectorXd &dnu) const |
| double | lineSearchGeneral (const VectorXd &x, const VectorXd &dx, const VectorXd &nu, const VectorXd &dnu) const |
| void | solveKKTSystem (const MatrixXd &Hx, const MatrixXd &Hy, const MatrixXd &A, const VectorXd &c, const VectorXd &b, VectorXd &x, VectorXd &y) const |
| void | solveKKTSystem (const MatrixXd &Hx, const MatrixXd &A, const VectorXd &c, const VectorXd &b, VectorXd &x, VectorXd &y) const |
| Protected Attributes inherited from drwnQPSolver | |
| MatrixXd | _mP |
| positive definite quadratic term in the objective function | |
| VectorXd | _q |
| linear term in the objective function | |
| double | _r |
| constant term in the objective function | |
| MatrixXd | _mA |
| linear equality constraint matrix | |
| VectorXd | _b |
| linear equality constraint vector | |
| MatrixXd | _mG |
| linear inequality constraint matrix | |
| MatrixXd | _h |
| linear inequality constraint vector | |
| VectorXd | _l |
| variable lower bounds (box constraint) | |
| VectorXd | _u |
| variable upper bounds (box constraint) | |
| VectorXd | _x |
| current estimate of solution | |
Solves (small scale) quadratic programs by adding a log-barrier penalty
![\[ \phi(x) = \sum_k \log(h_k - g^T_k x) + \sum_i \log(x_i - l_i) + \sum_i \log(u_i - x_i) \]](form_53.png)
and iteratively solving
![\[ \begin{array}{ll} \textrm{minimize (over $x$)} & \frac{1}{2} x^T P x + q^T x + r - \frac{1}{t} \phi(x) \\ \textrm{subject to} & Ax = b \end{array} \]](form_54.png)
for increasing values of t.
1.8.6