APPENDIX D


 LCRAND-RANDQP SOLUTION ALGORITHM


 The solution algorithm used by LCRAND (and RANDQP) uses a modified
version of the Wolfe method [6]. The tableau structure that is used
internally is depicted below. Note that the program converts everything
 1 1
into "less than or equal to" constraints. The x, w w P and P
columns are kept nonnegative throughout. W2 may have negative activities
during the solution process, but must finally become all non-negative
when an "equilibrium" solution is reached. The p vectors may be non-neg-
ative at anytime because they are the dual variables associated with equality
rows in the primal problem. The following conditions are maintained
at all times:
 2
 xw = 0
 1
 w P = 0
 + +

 w P =0

The algorithm proceeds as described in steps 1 through 4 below.
1. Find a feasible solution for the primal subproblem
 A2x < b
 1
 Ax > b

 A3x = b3

2. Extend the basis to include appropriate dual variables in a manner
 which ensures a complementary solution. (See Figure 13).
 2
 a. For every non-basic x, insert the w (slack) variable associated
 with it.
 1 1
 b. For every nonbasic w+ w insert the appropriate p+, p
 variable.
 c. Insert all of the unrestricted variables in the basis.