The NLPC Nonlinear Optimization Solver |
Feasible Starting Point
You can specify a starting point for the optimization. If the specified point is
infeasible to linear and/or bound constraints, two schemes are used to obtain a feasible
starting point (feasible to linear and bound constraints only), depending on the type of
problem. They are as follows.
- When only bound constraints are specified:
- If the variable
,
, violates a
two-sided bound constraint
,
the variable is given a new value inside the feasible
interval, as follows:
![x_i = \{ l_i, & {\rm if \:} u_i = l_i \ l_i + \frac{1}2(u_i - l_i), & {\rm ... ...i \lt 4 \ l_i + \frac{1}{10}(u_i - l_i), & {\rm if \:} u_i - l_i \ge 4 .](images/cnlp_cnlpeq152.gif)
- If the variable
,
, violates a
one-sided bound constraint
or
,
the variable is given a new value near the violated bound,
as follows:
![x_i = \{ l_i + \max\{1,\frac{1}{10}l_i\}, & {\rm if \:} x_i \lt l_i \ u_i - \max\{1,\frac{1}{10}u_i\}, & {\rm if \:} x_i \gt u_i .](images/cnlp_cnlpeq155.gif)
- When general linear constraints are specified, the scheme to find a feasible
starting point involves two algorithms that 1) find a feasible point independent of
the starting point or 2) find a feasible point closest to the starting point. Both
algorithms are active set methods.
Copyright © 2008 by SAS Institute Inc., Cary, NC, USA. All rights reserved.