mentation has been provided than was previously available for RANDQP
(LCRAND's predecessor) [4].


 2. DESCRIPTION OF LINEAR AND NONLINEAR MODELS


 Both linear and quadratic programming can be considered special
cases of the more general problem of linear complementarity programming
(LCP) [l,p. 1]. LCRAND was developed to solve an LCP type problem
arising from economic models involving international trade. Although
LCRAND will solve LP and QP problems efficiently, there are algorithmic
and economic aspects of LCP which make it distinctly different in approach
from the tradition of linear programming. We will examine briefly the
nature of LP, QP, and LCP with reference to economic and mathematical
considerations in order to illuminate the differences between them, and
to identify the common thread which runs throughout.


2.1 General Non-Linear Programming


 A standard general non-linear programming (NLP) problem can be stated
as follows:
 Find x that maximizes f(x) subject to g(x) > 0 and x > 0,
where
 f(x) is a single valued continuous and differentiable function of
 x e Rn (an n dimensional real space) and g(x) is an n vector function
 of m continuous and differentiable functions gi(x), i = 1, 2, ..., m.
 We know that by the Kuhn-Tucker theory of NLP, if the following
 saddle value problem (SVP) has a solution as stated, the x part of the
 saddle point is a solution of the NLP [5, Chapt. 2]:

 Find a saddle point (x, p) that satisfies the saddle value property
 that


 LCRAND is actually a modified version of the RANDQP program. The
 specific differences are described in Appendix C.