Feasible Starting Point
Two algorithms are used to obtain a feasible starting point.
- When only boundary constraints are specified:
- If the parameter
,
, 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, & {\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 .](images/nlp_nlpeq350.gif)
- If the parameter
,
, 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, \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 .](images/nlp_nlpeq354.gif)
- 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.
Copyright © 2008 by SAS Institute Inc., Cary, NC, USA. All rights reserved.