LINPROG fails to converge for some problems

[Allez-y]

Dear Johan,

I would like to know why LINPROG fails to compute the optimal solution for the following problems:

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% First example: true optimal solution X* = [3 0]', J* = 6 --> LINPROG returns X = [ ], J = [ ]

c = -[2 1];

Ad = [1 1 ; -1 0];

bd = [3 -2]';

options = optimoptions('linprog','Algorithm','dual-simplex');

[X, J, exitflag] = linprog(c,Ad,bd,[],[],[],[],[],options);

% Second example: true optimal solution X* = [0 3]', J* = -6 --> LINPROG returns X = [-1 3]', J = -7

c = [1 -2];

Ad = [-1 -1 ; 1 -1 ; 0 1];

bd = [-2 -1 3];

options = optimoptions('linprog','Algorithm','dual-simplex');

[X, J, exitflag] = linprog(c,Ad,bd,[],[],[],[],[],options);

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Thanks.

[Allez-y]

I'm so sorry, I have understood my mistake. I thought LINPROG worked on x >= 0 by default. In fact, I must enforce such constraint too.

So doing, we obtain:

% First example:

c = -[2 1];

Ad = [1 1 ; -1 0 ; -1 0 ; 0 -1];

bd = [3 -2 0 0]';

options = optimoptions('linprog','Algorithm','dual-simplex');

[X, J, exitflag] = linprog(c,Ad,bd,[],[],[],[],[],options);

% Second example:

c = [1 -2];

Ad = [-1 -1 ; 1 -1 ; 0 1; -1 0 ; 0 -1];

bd = [-2 -1 3 0 0];