Procedures

Given an m by n matrix, $\mathbf{A}$, and an m-vector, $\mathbf{b}$, compute an n-vector, $\mathbf{x}$, that solves the least squares problem:

Call bvls, but matching the interface of the old nnls.

Check for convergence.

constant times a vector plus a vector. uses unrolled loops for increments equal to one.

copies a vector, x, to a vector, y. uses unrolled loops for increments equal to one.

forms the dot product of two vectors. uses unrolled loops for increments equal to one.

Destructor for linmin_data type.

destructor for slsqp_solver.

Destructor for slsqpb_data type.

Function that returns the Euclidean norm $\sqrt{ \mathbf{x}^T \mathbf{x} }$ of a vector $\mathbf{x}$.

scales a vector by a constant. uses unrolled loops for increment equal to one.

enforce the bound constraints on x.

Compute orthogonal rotation matrix.

Construction and/or application of a single householder transformation $Q = I + u(u^t)/b$.

Rank-deficient least squares algorithm using householder forward triangulation with column interchanges.

initialize the slsqp_solver class. see slsqp for more details.

$LDL^T$ - rank-one - update

Least distance programming routine. Minimize $\frac{1}{2} \mathbf{x}^T \mathbf{x}$ subject to $\mathbf{G} \mathbf{x} \ge \mathbf{h}$.

Linesearch without derivatives (used by slsqp if linesearch_mode=2). Returns the abscissa approximating the point where f attains a minimum.

for mode=1, the subroutine returns the solution x of equality & inequality constrained least squares problem lsei :

for mode=1, the subroutine returns the solution x of inequality constrained linear least squares problem:

Minimize $|| e x - f ||$ with respect to $x$, with upper triangular matrix $e = + d ^{1/2} l^T$, and vector $f = -d^{-1/2} l^{-1} g$, where the unit lower tridiangular matrix $l$ is stored columnwise dense in the $n*(n+1)/2$ array $l$ with vector $d$ stored in its 'diagonal' thus substituting the one-elements of $l$

Convert the slsqp mode flag to a message string.

Nonnegative least squares algorithm.

Report a message from an slsqp_solver class. This uses the iprint variable in the class as the unit number for printing. Note: for fatal errors, if no unit is specified, the error_unit is used.

slsqp: sequential least squares programming to solve general nonlinear optimization problems

main routine for calling slsqp.

nonlinear programming by solving sequentially quadratic programs

A method that the user can call to stop the iterations. (it can be called in any of the functions). SLSQP will stop at the end of the next iteration.