PROC NLP: Feasible Starting Point :: SAS/OR(R) 9.2 User's Guide: Mathematical Programming

The NLP Procedure

Feasible Starting Point

Two algorithms are used to obtain a feasible starting point.

When only boundary constraints are specified:
- If the parameter , $1 \leq j \leq n$ , violates a two-sided boundary constraint (or an equality constraint) $l_j \leq x_j \leq u_j$ , the parameter is given a new value inside the feasible interval, as follows:
  $x_j = \{ l_j, & {\rm if \: } u_j \leq l_j \ l_j + \frac{1}2(u_j - l_j), & {... ...\lt 4 \ l_j + \frac{1}{10}(u_j - l_j), & {\rm if \: } u_j - l_j \geq 4 .$
- If the parameter , $1 \le j \le n$ , violates a one-sided boundary constraint $l_j \leq x_j$ or $x_j \leq u_j$ , the parameter is given a new value near the violated boundary, as follows:
  $x_j = \{ l_j + \max(1, \frac{1}{10}l_j), & {\rm if \: } x_j \lt l_j \ u_j - \max(1, \frac{1}{10}u_j), & {\rm if \: } x_j \gt u_j .$
When general linear constraints are specified, the algorithm of Schittkowski and Stoer (1979) computes a feasible point, which may be quite far from a user-specified infeasible point.