Using an expansion

In some case it may be interesting to consider an expansion of the function around a given point. For example consider the term $x^2$ with $x$ in the range [1,2]: in the simplex method the range [1,4], for this term will be added to the non linear part of the equation. But if we substitute the unknown $x$ by a new unknown $x_1$ such that $x=1+x_1$ (hence the range for $x_1$ will be [0,1]) we will get $x^2=1+2x_1+x_1$ we will get an additional linear term ($2x_1$) while the non linear part will be $x_1^2$ with the range [0,1]. For each variable $y_i$ in the range $[\underline{y_i},\overline{y_i}]$ we may define a new variable $y^1_i$ such that $y_i =\underline{y_i}+y^1_i$ where $y^1_i$ has the range $[0,\overline{y_i}-\underline{y_i}]$. We may then write the non linear and linear procedures for the unknowns $y^1_i$ but it necessary to notify the simplex procedure that such an expansion is used. This is done by setting the flag ALIAS_Simplex_Expanded to 1 (this possibility is available only for the simplex method using the gradient).

You may also prohibit the use of the simplex method in the procedure (for example to use it only in your own simplification procedure) by setting the flag ALIAS_DONT_USE_SIMPLEX to 1.