LSSOL 1.05 - Description

LSSOL (invented by Philip Gill, Walter Murray, Michael Saunders and Margaret Wright) is a software package for solving constrained linear least-squares problems and convex quadratic programs (definite or semi definite), including linear programs. Dense matrices are assumed throughout LSSOL is recommended for QP problems whose objective


includes a term of the form x'A'Ax for some matrix A (which may be rectangular, square or triangular).

Linear constraints and bounds on the variables are treated separately by an active-set method. If the problem has no feasible solution, LSSOL minimizes the sum of the constraint and bound violations.



A two-phase (primal) quadratic programming
method is used, with features to exploit the convexity of the objective function. LSSOL may also be used for linear programming and to find a feasible point with respect to a set of linear equality and inequality constraints. LSSOL treats all matrices as dense, and hence is not intended for large sparse problems.


LSSOL requires the quadratic to be positive definite or semi definite  On the other hand QPOPT can be used for general QP problems (but may find just a local minimum).  LSSOL is contained in the nonlinear programming package NPSOL.


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