APPENDIX C


 USE OF RANDQP


 Since the basic algorithm and control cards in LCRAND have not been
altered from the original RANDQP, this manual can be used in working with
the original RANDQP code. There are several things that must be kept in
mind, however, that are different between the two programs. Aside from
the fact that the multiple run procedure described in Section6 will not
work with the RANDQP, the differences lie primarily in the conventions
for inputting the problem matrix data.
 The RANDQP assumes a quadratic function of the form c'x + x'Qx
whereas the more natural one c'x 1/2x'Qx was described above. The user
should follow the sign rules as described in Section 4, however, the
following additional rules must be followed.
 a) If an asymmetric Q matrix is inserted into the RANDQP, it will
 use 1/2(Q + Q ).
 b) All diagonal coefficients arising from demand & supply functions
 (i.e. where an integration is involved) must be premultiplied by
 1/2.
 c) Only one triangle (upper or lower) of the Q matrix needs to be
 specified explicitly. The code will generate the corresponding
 symmetric part. If this option is taken (only one triangle
 specified) then the off-diagonal elements should not be multiplied
 by 1/2 if coming from a demand or supply function (in contrast
 to diagonal elements as in b). If the entire Q matrix is entered
 and it consists of demand and supply function coefficients, then
 the entire matrix should be premultiplied by 1/2 before insertion.
 The reasoning behind the above is as follows. Because the RANDQP
assumes the c'x + x'Qx objective function, it does the following to
ensure the Kuhn-Tucker conditions are generated in a consistent manner.