A computational analysis of LCP methods for bilinear and concave quadratic programming

The use of a sequential linear complementarity problem (SLCP) algorithm for finding a global minimum of bilinear programming problem (BLP) or a concave quadratic program (CQP) is examined. The algorithm consists of solving a sequence of linear complementarity problems (LCP). A branch-and-bound method is also considered in this study. This algorithm is based on the reformulation of a BLP into an LCP with a linear function to minimize. Computational experience with small and medium scale BLPs and CQPs indicates that the SLCP algorithm is quite efficient in finding a global minimum (or at least a solution that is quite near the optimum), but it is, in general, unable to establish that such a solution has been found. An algorithm to find a lower-bound for the BLP can overcome this drawback in some cases. Furthermore the SLCP algorithm is shown to be robust and compares favorably with the branch-and-bound method and another alternative technique.