slsqp_core Module

mode value if converged

mode value if not converged

if the SQP problem is inconsistent (will return not_converged)

controls reverse communication must be set to 0 initially, returns with intermediate values 1 and 2 which must not be changed by the user, ends with convergence with value 3.

left endpoint of initial interval

right endpoint of initial interval

function value at linmin which is to be brought in by reverse communication controlled by mode

desired length of interval of uncertainty of final result

is the total number of constraints, $m \ge 0$

is the number of equality constraints, $m_{eq} \ge 0$

see a, $la \ge \max(m,1)$

is the number of variables, $n \ge 1$

x() stores the current iterate of the n vector x on entry x() must be initialized. on exit x() stores the solution vector x if mode = 0.

xl() stores an n vector of lower bounds xl to x.

xu() stores an n vector of upper bounds xu to x.

is the value of the objective function.

c() stores the m vector c of constraints, equality constraints (if any) first. dimension of c must be greater or equal la, which must be greater or equal max(1,m).

g() stores the n vector g of partials of the objective function; dimension of g must be greater or equal n+1.

the la by n + 1 array a() stores the m by n matrix a of constraint normals. a() has first dimensioning parameter la, which must be greater or equal max(1,m).

abs(acc) controls the final accuracy. if acc < zero an exact linesearch is performed, otherwise an armijo-type linesearch is used.

prescribes the maximum number of iterations. on exit iter indicates the number of iterations.

mode controls calculation:

w() is a one dimensional working space. the first m+n+n*n1/2 elements of w must not be changed between subsequent calls of slsqp. on return w(1) ... w(m) contain the multipliers associated with the general constraints, while w(m+1) ... w(m+n(n+1)/2) store the cholesky factor l*d*l(t) of the approximate hessian of the lagrangian columnwise dense as lower triangular unit matrix l with d in its 'diagonal' and w(m+n(n+1)/2+n+2 ... w(m+n(n+1)/2+n+2+m+2n) contain the multipliers associated with all constraints of the quadratic program finding the search direction to the solution x*

the length of w, which should be at least:

data for slsqpb.

data for linmin.

min $\alpha$ for line search $0 < \alpha_{min} < \alpha_{max} \le 1$

max $\alpha$ for line search $0 < \alpha_{min} < \alpha_{max} \le 1$

stopping criterion if $|f| < tolf$ then stop.

stopping criterion if $|f_{n+1} - f_n| < toldf$ then stop.

stopping criterion if $||x_{n+1} - x_n|| < toldx$ then stop.

maximum number of iterations in the nnls problem

which NNLS method to use

"infinity" for the upper and lower bounds. if xl<=-infinite_bound or xu>=infinite_bound then these bounds are considered nonexistant. If infinite_bound=0 then huge() is used for this.

in: maximum number of iterations. out: actual number of iterations.

dim(w) =

data for linmin.

min $\alpha$ for line search $0 < \alpha_{min} < \alpha_{max} \le 1$

max $\alpha$ for line search $0 < \alpha_{min} < \alpha_{max} \le 1$

stopping criterion if $|f| < tolf$ then stop.

stopping criterion if $|f_{n+1} - f_n| < toldf$ then stop

stopping criterion if $||x_{n+1} - x_n|| < toldx$ then stop

maximum number of iterations in the nnls problem

which NNLS method to use

"infinity" for the upper and lower bounds.

stores the n-dimensional solution vector

stores the vector of lagrange multipliers of dimension m+n+n (constraints+lower+upper bounds)

is a success-failure flag with the following meanings:

maximum number of iterations in the nnls problem

which NNLS method to use

"infinity" for the upper and lower bounds.

stores the solution vector

stores the residuum of the solution in euclidian norm

on return, stores the vector of lagrange multipliers in its first mc+mg elements

is a success-failure flag with the following meanings:

maximum number of iterations in the nnls problem

which NNLS method to use

stores the solution vector

stores the residuum of the solution in euclidian norm

stores the vector of lagrange multipliers in its first mg elements

is a success-failure flag with the following meanings:

maximum number of iterations in the nnls problem

which NNLS method to use

on entry g stores the m by n matrix of linear inequality constraints. g has first dimensioning parameter mg

the right side of the inequality system.

solution vector x if mode=1.

euclidian norm of the solution vector if computation is successful

w is a one dimensional working space, the length of which should be at least (m+2)*(n+1) + 2*m. on exit w stores the lagrange multipliers associated with the constraints. at the solution of problem ldp.

success-failure flag with the following meanings:

maximum number of iterations in the nnls problem

which NNLS method to use

on entry, contains the m by n matrix, a. on exit, contains the product matrix, q*a, where q is an m by m orthogonal matrix generated implicitly by this subroutine.

first dimensioning parameter for the array a.

on entry, contains the m-vector b. on exit, contains q*b.

the solution vector.

euclidean norm of the residual vector.

array of working space. on exit w will contain the dual solution vector. w will satisfy w(i) = 0 for all i in set p and w(i) <= 0 for all i in set z.

an m-array of working space.

this is a success-failure flag with the following meanings:

maximum number of iterations (if <=0, then 3*n is used)

the array a initially contains the $m \times n$ matrix $\mathbf{A}$ of the least squares problem $\mathbf{A} \mathbf{x} = \mathbf{b}$. either m >= n or m < n is permitted. there is no restriction on the rank of a. the matrix a will be modified by the subroutine.

the first dimensioning parameter of matrix a (mda >= m).

if nb = 0 the subroutine will make no reference to the array b. if nb > 0 the array b must initially contain the m x nb matrix b of the the least squares problem ax = b and on return the array b will contain the n x nb solution x.

first dimensioning parameter of matrix b (mdb>=max(m,n))

absolute tolerance parameter for pseudorank determination, provided by the user.

pseudorank of a, set by the subroutine.

on exit, rnorm(j) will contain the euclidian norm of the residual vector for the problem defined by the j-th column vector of the array b.

array of working space

array of working space

1 or 2 -- selects algorithm h1 to construct and apply a householder transformation, or algorithm h2 to apply a previously constructed transformation.

the index of the pivot element

if l1 <= m the transformation will be constructed to zero elements indexed from l1 through m. if l1 > m the subroutine does an identity transformation.

see li.

on entry with mode = 1, u contains the pivot vector. iue is the storage increment between elements. on exit when mode = 1, u and up contain quantities defining the vector u of the householder transformation. on entry with mode = 2, u and up should contain quantities previously computed with mode = 1. these will not be modified during the entry with mode = 2. dimension[u(iue,m)]

see u.

see u.

on entry with mode = 1 or 2, c contains a matrix which will be regarded as a set of vectors to which the householder transformation is to be applied. on exit c contains the set of transformed vectors.

storage increment between elements of vectors in c.

storage increment between vectors in c.

number of vectors in c to be transformed. if ncv <= 0 no operations will be done on c.

order of the coefficient matrix a

In: positive definite matrix of dimension n; only the lower triangle is used and is stored column by column as one dimensional array of dimension n*(n+1)/2.

vector of dimension n of updating elements.

scalar factor by which the modifying dyade $z z^T$ is multiplied.

working array of dimension n (used only if $\sigma \lt 0$ ).

optimization variable vector

lower bounds (must be same dimension as x)

upper bounds (must be same dimension as x)

"infinity" for the upper and lower bounds. Note that NaN may also be used to indicate no bound.