QL solves quadratic programming problems with a positive definite objective function matrix and linear equality and inequality constraints.

The algorithm is an implementation of the dual method of Goldfarb and Idnani and a modification of the original implementation of Powell. Initially, the algorithm computes a solution of the unconstrained problem by performing a Cholesky decomposition and by solving the triangular system. In an iterative way, violated constraints are added to a working set and a minimum with respect to the new subsystem with one additional constraint is calculated. Whenever necessary, a constraint is dropped from the working set. The internal matrix transformations are performed in numerically stable way.

QL is a FORTRAN subroutine where all data are passed by subroutine arguments.

• separate handling of upper and lower bounds
• initially given Cholesky decomposition exploited
• full documentation
• FORTRAN source code (close to F77, conversion to C by f2c possible)

As an essential part of the nonlinear programming routine NLPQLP, QL solves the internal quadratic programming subproblem of the SQP-method and has therefore the same domain of application as NLPQLP.

• M.J.D. Powell, On the quadratic programming algorithm of Goldfarb and Idnani, Report DAMTP 1983/Na 19, University of Cambridge, Cambridge (1983))
• K. Schittkowski, QL: A Fortran code for convex quadratic programming - User's guide, Version 2.11, Report, Department of Mathematics, University of Bayreuth (2005)