Users guide for sqopt version 7: software for largescale linear and 16 programming, Availableonlinevia¡http://www.cam.ucsd.edu/peg/sqdoc7.pdf¿[accessedAugust7

SQOPT is a software package for minimizing a convex quadratic function subject to both equality and inequality constraints. SQOPT may also be used for linear pro-gramming and for finding a feasible point for a set of linear equalities and inequalities. SQOPT uses a two-phase, active-set, reduce-Hessian method. It is most efficient on problems with relatively few degrees of freedom (for example, if only some of the vari-ables appear in the quadratic term, or the number of active constraints and bounds is nearly as large as the number of variables). However, unlike previous versions of SQOPT, there is no limit on the number of degrees of freedom. SQOPT is primarily intended for large linear and quadratic problems with sparse constraint matrices. A quadratic term 1 2 xTHx in the objective function is represented by a user subroutine that returns the product Hx for a given vector x. SQOPT uses stable numerical methods throughout and includes a reliable basis package (for maintaining sparse LU factors of the basis matrix), a practical anti-degeneracy procedure, scaling, and elastic bounds on any number of constraints and variables. SQOPT is part of the SNOPT package for large-scale nonlinearly constrained op-timization. The source code is re-entrant and suitable for any machine with a Fortran compiler (or the f2c translator and a C compiler). SQOPT may be called from a driver program in Fortran, C, or Matlab. It can also be used as a stand-alone pack-age, reading data in the MPS format used by commercial mathematical programming systems