# GAMS Support Wiki

### Site Tools

gams:using_gams_for_solving_square_nonlinear_systems

# Differences

This shows you the differences between two versions of the page.

 gams:using_gams_for_solving_square_nonlinear_systems [2007/10/19 09:22]127.0.0.1 external edit gams:using_gams_for_solving_square_nonlinear_systems [2007/10/20 07:14]Franz Nelissen 2020/05/28 08:37 Michael Bussieck 2007/10/20 07:14 Franz Nelissen 2007/10/19 09:22 external edit 2020/05/28 08:37 Michael Bussieck 2007/10/20 07:14 Franz Nelissen 2007/10/19 09:22 external edit Last revision Both sides next revision Line 4: Line 4: and ''​i = 1,..., n''​.//​ and ''​i = 1,..., n''​.//​ - Contributed by [[tom@mpsge.org|Tom Rutherford]]:​ There are three basic approaches ​ available for solving square + Contributed by [[tom@mpsge.org|Tom Rutherford]] to the [[http://​www.gams.com/​maillist/​gams_l.htm|GAMS-User List]]: There are three basic approaches ​ available for solving square nonlinear systems under GAMS: nonlinear systems under GAMS: Line 15: Line 15: 3) Formulate as a CNS (constrained nonlinear system):​\\ ​ 3) Formulate as a CNS (constrained nonlinear system):​\\ ​ - ​f_i(x) = 0 i=1,​...,​n  ​''​\\ + ​f_i(x) = 0 i=1,​...,​n ​ - xlo_i <= x_i <= xup_i ''​ + xlo_i <= x_i <= xup_i Approaches (1) and (3) offer some advantages if the functions you are using are undefined for some values of x. You can then apply upper and lower bounds which assure that the algorithm does not wander off, but even with bounds you may not be assured of finding solution if the functions are not nicely behaved (monotone, P, etc.). Approaches (1) and (3) offer some advantages if the functions you are using are undefined for some values of x. You can then apply upper and lower bounds which assure that the algorithm does not wander off, but even with bounds you may not be assured of finding solution if the functions are not nicely behaved (monotone, P, etc.).