QL

Convex quadratic programming

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.

Special features of QL are

• separate handling of upper and lower bounds;
• exploiting predefined Cholesky decompositions;
• FORTRAN source code;
• full documentation by in-source comments.

QL is a double precision FORTRAN-77 subroutine where all data are passed by subroutine arguments.

Need more info?

Prof. K. Schittkowski 
Dept. of Mathematics
University of Bayreuth 
95440 Bayreuth, Germany 
Klaus.Schittkowski@uni-bayreuth.de

Reference:

M.J.D. Powell, On the quadratic programming algorithm of Goldfarb and Idnani, Report DAMTP 1983/Na 19, University of Cambridge, Cambridge (1983).

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