octave使用glpk求解线性规划

调用[xval, fval, status, extra] = glpk (c, A, b, lb, ub, ctype, vartype, sense, param);

max/min f = c * x
A * x [>=,<= …] b

LB：x最小取值
UB：x最大取值

ctype：规定A*x与 b的关系，

“F”
A free (unbounded) constraint (the constraint is ignored).
“U”
An inequality constraint with an upper bound (A(i,:)*x <= b(i)).
“S”
An equality constraint (A(i,:)*x = b(i)).
“L”
An inequality with a lower bound (A(i,:)*x >= b(i)).
“D”
An inequality constraint with both upper and lower bounds (A(i,:)*x >= -b(i)) and (A(i,:)*x <= b(i)).

vartype：x变量是浮点数还是整数，’C‘为浮点数，‘I’为整型变化。

sense ：为-1 最大化目标函数，为1最小化目标函数

param用法可参考自带文档
其中param.itlim 可以限制迭代次数，如果问题比较复杂，通过设置itlim可求近似解

c=[1.0445;1.3989;3.3211;1.0640;1.4662;3.4043;1.1255;2.8009;3.3211;1.1130;1.3590;2.8551;1.0312;1.1314;2.4428]';
b = 8000*[0.2;0.1;0.1;0.1;0.1;1;2.5;10]';

A = [ 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0;
     0 0 0 1 1 1 0 0 0 0 0 0 0 0 0;
     0 0 0 0 0 0 1 1 1 0 0 0 0 0 0;
     0 0 0 0 0 0 0 0 0 1 1 1 0 0 0;
     0 0 0 0 0 0 0 0 0 0 0 0 1 1 1;
     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
     5 5 5 2 2 2 4 4 4 3 3 3 1 1 1;
     2 9 20 3 12 25 4 15 20 4 9 18 2 5 18];
lb = zeros(15,1);%x最小是0
ub = lb+8000;%x不超过8000，默认不超过inf
ctype = "LLLLLULU";
vartype = "CCCCCCCCCCCCCCC";
sense = -1; %maximization

param.msglev = 3;  % output all

%param.itlim = 1000;

[xval, fval, status, extra] = ...
   glpk (c, A, b, lb, ub, ctype, vartype, sense, param);