<(x, p) (O(x, p) <(x, p) for x > 0 and p > 0, where O(x, p) E f(x) + p'g(x). Thus, instead of approaching NLP per se, (whose solution algorithms are known to be"quite restricted), it will be worthwhile to approach it from the SVP side. The necessary conditions (usually called the Kuhn-Tucker conditions) for (x, p) to be a saddle point are as follows: (NL1) < 0 and ix = 0 i- x (NL2) 4> 0 and 41p = 0 p (NL3) R > 0 and p> 0, where ( and >. are an (n x 1) vector, [ao/ax ...1D/ax b] - P=P and an (m x 1) vector, [/apl... /p' 1p x= respectively. P=P Thus, if x and F are found to satisfy (NL1), (NL2) and (NL3), we have to check if R is actually a maximizing solution of the NLP. This is guaranteed if (NL4) each of f(x) and gi(x), i = 1, 2, ..., m, is a concave function of x. Another natural condition for the existence of a solution for the NLP problem is (NL5) the feasibility set X = {xjg(x) > 0 and x > 0} is non-empty, Sometimes the uniqueness of a solution may be of interest. The following condition (along with NL4 and NL5) will answer this question: f(x) is strictly concave in x E X. (NL6)