Feasible Starting Point
Two algorithms are used to obtain a feasible starting point.
- When only boundary constraints are specified:
- If the parameter xj,
, violates a
two-sided boundary constraint (or an equality constraint)
, the parameter is given a
new value inside the feasible interval, as follows:
![x_j = & l_j , &
{if u_j \leq l_j\space } \ x_j = & l_j + {1 \over 2}(u_j - l_j)...
...l_j \lt 4} \ x_j = & l_j + {1 \over 10}(u_j - l_j) , &
{if u_j - l_j \geq 4}](images/nlpeq139.gif)
- If the parameter xj, j = 1, ... ,n, violates a
one-sided boundary constraint
or
, the parameter is given a new value near the violated boundary,
as follows:
![x_j = & l_j + \max(1, {1 \over 10}l_j) , &
{if l_j\space violated} \ x_j = & u_j - \max(1, {1 \over 10}u_j) , &
{if u_j\space violated}](images/nlpeq142.gif)
- When general linear constraints are specified, a feasible point
is computed by the algorithm of Schittkowski and Stoer (1979),
that may be quite far from a user-specified infeasible
point.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.