Re: LinearProgramming[]
- To: mathgroup at smc.vnet.net
- Subject: [mg123554] Re: LinearProgramming[]
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Sun, 11 Dec 2011 03:46:18 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201112091058.FAA03920@smc.vnet.net>
- Reply-to: drmajorbob at yahoo.com
> I believe that you will find that if these strict constraints have any > effect on an optimization problem, the effect will be that there is > no unique solution to the problem --- this applies to both linear and > nonlinear optimization problems. No OPTIMAL solution, actually... unique or not. Bobby On Sat, 10 Dec 2011 06:28:53 -0600, Virgil Stokes <vs at it.uu.se> wrote: > On 09-Dec-2011 11:58, é�â?? 厚 wrote: >> We know all constraints in LinearProgramming[] involve ">=" or "<=". >> >> How can I solve the following problem with LinearProgramming[]: >> >> Assuming x+2y-z>0,x+y-z>=60,y+2z>12,x>0,y>0 and z>1 >> >> we want to get the minimum of 2x+3y+4z in the abrove constraints. >> >> Note that there are ">" other than">=" in the constraints we have >> given. >> > If an LP problem has a unique optimal solution then it must lie along the > boundary of a polyhedron formed by the constraints. This implies that > strictly > less than (<) or strictly greater than (>) constraints do not fit into a > LP > problem formulation; i.e. the solution is no longer guaranteed to be > along a > boundary. This means that the function LinearProgramming is not > applicable for > "<" and ">" constraints. > > I believe that you will find that if these strict constraints have any > effect on > an optimization problem, the effect will be that there is no unique > solution to > the problem --- this applies to both linear and nonlinear optimization > problems. > Thus, I suggest that you try to reformulate your problem such that it > can be > written without any strict constraints. Here is your problem > reformulated with > ">" replaced by ">=". > > m = {{1, 2, -1}, {1, 1, -1}, {0, 1, 2}}; > b = {0, 60, 12}; s = {1, 1, 1}; > c = {2, 3, 4}; > bs = Transpose[{b, s}]; > LinearProgramming[c, m, bs, {0, 0, 1}] > > which gives {51,10,1} as the solution to, > > minimize 2x + 3y + 4z > subject to: > x + 2y - z >= 0 > x + y - z >= 60 > y + 2z >= 12 > x >= 0, y >= 0, z >= 1 > > Note, two of the constraints (6 in total) in your original problem are > not > satisfied. It might useful for you to plot the polyhedron formed by these > constraints --- graphical analysis can be enlightening. > -- DrMajorBob at yahoo.com
- References:
- LinearProgramming[]
- From: é å <shlwell1988@gmail.com>
- LinearProgramming[]