0
problem with fot_linprog
[Scilab 6.1.1, FOT v.0.4.1, windows 10]
Let's take a simple example to illustrate the problem:
A = [6, 15, 6; 14, 42, 16; 2, 8, 2];
B = [9; 21; 4]; C = [10; -7; -5]; LB = [0, 0, 0];
[xopt, zmin, exitflag, output, lambda]= fot_linprog (C, A, B, [], [], LB, []);
Everything works fine, except Lagrange multipliers from lambda:
--> disp(lambda.ineqlin);
0.
-0.3125
0.
The correct answer should be [0; +0.3125; 0] (checked by manual calculation and by means of karmarkar)
Dear experts, can someone tell me what I'm doing wrong? Or is this a fot_linprog bug and would it be better to use another tool?
Scilab Toolbox Optimization Toolbox
0More than 60 people have viewed my question, thank you for your interest in this topic. Unfortunately, I have not yet received an answer to my question, so I am trying to figure out the problem in fot_linprog.
My test: C=[1;1]; Aeq=[2, 1]; Beq=[1]; A=[2;-1]; B=[0]; LB=[0;0].
I have tried four methods: 1) manually; 2) Matlab (linprog); 3) Scilab (fot_linprog); 4) Scilab (karmarkar).
The results are as follows: xopt and fopt matched in all cases.
Dual problem: yopt have the same modulus but differ in sign (yopt.eqlin and yopt.ineqlin):
3/4 and 1/4, manual calculation;
-0.75 and 0.25, (Matlab, linprog);
0.75 and-0.25 (Scilab, fot_linprog);
-0.75 and 0.25 (Scilab, karmarkar).
Carefully reading the documentation for the primal-dual LP problem in scilab and some other solvers, I found important (as it seems to me) information about the formulation of the dual problem in linprog (matlab): "...This sign convention matches that of nonlinear solvers (see Constrained Optimality Theory). However, this sign is the opposite of the sign in much linear programming literature, so a linprog Lagrange multiplier is the negative of the associated "shadow price"..."
In this comparison, Scilab (karmarkar) provides the same result as Matlab (linprog). The Scilab solver (fot_linprog) produces a completely different result in sign for yopt. Nothing about this was found in the documentation of fot_linprog (Scilab). Any help?
My test: C=[1;1]; Aeq=[2, 1]; Beq=[1]; A=[2;-1]; B=[0]; LB=[0;0].
I have tried four methods: 1) manually; 2) Matlab (linprog); 3) Scilab (fot_linprog); 4) Scilab (karmarkar).
The results are as follows: xopt and fopt matched in all cases.
Dual problem: yopt have the same modulus but differ in sign (yopt.eqlin and yopt.ineqlin):
3/4 and 1/4, manual calculation;
-0.75 and 0.25, (Matlab, linprog);
0.75 and-0.25 (Scilab, fot_linprog);
-0.75 and 0.25 (Scilab, karmarkar).
Carefully reading the documentation for the primal-dual LP problem in scilab and some other solvers, I found important (as it seems to me) information about the formulation of the dual problem in linprog (matlab): "...This sign convention matches that of nonlinear solvers (see Constrained Optimality Theory). However, this sign is the opposite of the sign in much linear programming literature, so a linprog Lagrange multiplier is the negative of the associated "shadow price"..."
In this comparison, Scilab (karmarkar) provides the same result as Matlab (linprog). The Scilab solver (fot_linprog) produces a completely different result in sign for yopt. Nothing about this was found in the documentation of fot_linprog (Scilab). Any help?
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