Procedures

This subroutine initializes iwhere and projects the initial x to the feasible set if necessary.

This subroutine computes the product of the 2m x 2m middle matrix in the compact L-BFGS formula of B and a 2m vector v; it returns the product in p.

For given x, l, u, g (with sbgnrm > 0), and a limited memory BFGS matrix B defined in terms of matrices WY, WS, WT, and scalars head, col, and theta, this subroutine computes the generalized Cauchy point (GCP), defined as the first local minimizer of the quadratic

This subroutine computes r=-Z'B(xcp-xk)-Z'g by using wa(2m+1)=W'(xcp-x) from subroutine cauchy.

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.

This subroutine finds a step that satisfies a sufficient decrease condition and a curvature condition.

This subroutine computes a safeguarded step for a search procedure and updates an interval that contains a step that satisfies a sufficient decrease and a curvature condition.

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

dpofa factors a real symmetric positive definite matrix.

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

dtrsl solves systems of the form

This subroutine checks the validity of the input data.

This subroutine forms the LEL^T factorization of the indefinite matrix:

This subroutine forms the upper half of the pos. def. and symm. T = thetaSS + LD^(-1)L', stores T in the upper triangle of the array wt, and performs the Cholesky factorization of T to produce JJ', with J' stored in the upper triangle of wt.

This subroutine counts the entering and leaving variables when iter > 0, and finds the index set of free and active variables at the GCP.

This subroutine sorts out the least element of t, and puts the remaining elements of t in a heap.

This subroutine calls subroutine dcsrch from the Minpack2 library to perform the line search. Subroutine dscrch is safeguarded so that all trial points lie within the feasible region.

This subroutine solves bound constrained optimization problems by using the compact formula of the limited memory BFGS updates.

This subroutine updates matrices WS and WY, and forms the middle matrix in B.

This subroutine prints the input data, initial point, upper and lower bounds of each variable, machine precision, as well as the headings of the output.

This subroutine prints out new information after a successful line search.

This subroutine prints out information when either a built-in convergence test is satisfied or when an error message is generated.

This subroutine computes the infinity norm of the projected gradient.

The main routine.

This routine contains the major changes in the updated version. The changes are described in the accompanying paper