RE: ConstrainedMin with negative variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg35148] RE: [mg35137] ConstrainedMin with negative variables*From*: "DrBob" <majort at cox-internet.com>*Date*: Wed, 26 Jun 2002 01:09:23 -0400 (EDT)*Reply-to*: <drbob at bigfoot.com>*Sender*: owner-wri-mathgroup at wolfram.com

It's usual to constrain LP variables to be non-negative because it simplifies the algorithm immensely and reduces the incidence of unbounded problems. It's not a real limitation, however, as the following demonstrates. First the result you obtained: objective = -7/3 x1 - 13/3 x2; constraints = {x1 + 5 x2 <= 0, -1 <= x1 <= 1, -1 <= x2 <= 1}; vars = Variables[objective]; ConstrainedMin[objective, constraints, vars] {0, {x1 -> 0, x2 -> 0}} Here's the substitution that generalizes it for you, and a solution in terms of the new variables: substitute = {x1 -> y1 - z1, x2 -> y2 - z2}; newVars = Variables[objective /. substitute]; ConstrainedMin[objective /. substitute, constraints /. substitute, newVars]; solution = Last[%] {y1 -> 1, y2 -> 0, z1 -> 0, z2 -> 1/5} Finally, in terms of the original variables: vars /. substitute /. solution {1, -(1/5)} That's the solution you wanted. Bobby Treat -----Original Message----- From: Markus Kolöchter [mailto:koloechter at web.de] To: mathgroup at smc.vnet.net Subject: [mg35148] [mg35137] ConstrainedMin with negative variables Hello ng, I'm trying to implement the method of Zoutendijk, which is to solve a nonlinear programming problem. Therefor I have to solve linear subproblems with the simplex method. But the Mathematica function "ConstrainedMin" assumes that all variables are non-negative. For example, I have the following input: ConstrainedMin[-7/3 x1 - 13/3 x2, {x1 + 5 x2 <= 0, -1 <= x1 <= 1, -1 <= x2 <= 1}, {x1, x2}] The Mathematica output is: {0, {x1 -> 0, x2 -> 0}} I think the proper result should be {-22/15, {x1 -> 1, x2 -> -1/5}}. If anyone has an idea, please let me know! Regards, Markus Kolöchter