對於python cvxopt 庫,這個庫用於求解線性和二次規劃。本節介紹如何求解線性規劃問題。
形如以下的問題：
我們將其寫成標準形式：
min cx
s.t. Ax < b
對應寫出A,b,c矩陣。
A = matrix([ [-1.0, -1.0, 0.0, 1.0], [1.0, -1.0, -1.0, -2.0] ])
b = matrix([ 1.0, -2.0, 0.0, 4.0 ])
c = matrix([ 2.0, 1.0 ])
要注意，這裏的matrix是cvx庫的matrix寫法，要求是按列從左到右書寫。
接下來調用標準的求解器solver.lp計算：
solvers.options['show_progress'] = True
sol=solvers.lp(c,A,b)
print(sol)
print(sol['x'])
結果如下：
pcost dcost gap pres dres k/t
0: 2.6471e+00 -7.0588e-01 2e+01 8e-01 2e+00 1e+00
1: 3.0726e+00 2.8437e+00 1e+00 1e-01 2e-01 3e-01
2: 2.4891e+00 2.4808e+00 1e-01 1e-02 2e-02 5e-02
3: 2.4999e+00 2.4998e+00 1e-03 1e-04 2e-04 5e-04
4: 2.5000e+00 2.5000e+00 1e-05 1e-06 2e-06 5e-06
5: 2.5000e+00 2.5000e+00 1e-07 1e-08 2e-08 5e-08
Optimal solution found.
{'x': <2x1 matrix, tc='d'>, 'y': <0x1 matrix, tc='d'>, 's': <4x1 matrix, tc='d'>, 'z': <4x1 matrix, tc='d'>, 'status': 'optimal', 'gap': 1.3974945737537904e-07, 'relative gap': 5.589978335863919e-08, 'primal objective': 2.499999989554308, 'dual objective': 2.4999999817312544, 'primal infeasibility': 1.1368786496881938e-08, 'dual infeasibility': 2.2578790069187308e-08, 'primal slack': 2.0388399547194678e-08, 'dual slack': 3.529915972560751e-09, 'residual as primal infeasibility certificate': None, 'residual as dual infeasibility certificate': None, 'iterations': 5}
[ 5.00e-01]
[ 1.50e+00]