5.3.4. Python 的QP建模与优化¶
在本节中，我们将使用 MindOpt Python 语言的 API 来建模以及求解 二次规划问题示例 中的问题。
5.3.4.1. 按行输入: mdo_qo_ex1¶
首先，引入 Python 包：
25from mindoptpy import *
并创建优化模型：
32 # Step 1. Create a model and change the parameters.
33 model = MdoModel()
接下来，我们通过 mindoptpy.MdoModel.set_int_attr() 将目标函数设置为 最小化 ，并调用 mindoptpy.MdoModel.add_var() 来添加四个优化变量，定义其下界、上界、名称和类型（有关 mindoptpy.MdoModel.set_int_attr() 和 mindoptpy.MdoModel.add_var() 的详细使用方式，请参考 Python 接口函数）：
36 # Step 2. Input model.
37 # Change to minimization problem.
38 model.set_int_attr(MDO_INT_ATTR.MIN_SENSE, 1)
39
40 # Add variables.
41 x = []
42 x.append(model.add_var(0.0, 10.0, 1.0, None, "x0", False))
43 x.append(model.add_var(0.0, MDO_INFINITY, 1.0, None, "x1", False))
44 x.append(model.add_var(0.0, MDO_INFINITY, 1.0, None, "x2", False))
45 x.append(model.add_var(0.0, MDO_INFINITY, 1.0, None, "x3", False))
接着，我们开始添加线性约束：
46 # Add constraints.
47 # Note that the nonzero elements are inputted in a row-wise order here.
48 model.add_cons(1.0, MDO_INFINITY, 1.0 * x[0] + 1.0 * x[1] + 2.0 * x[2] + 3.0 * x[3], "c0")
49 model.add_cons(1.0, 1.0, 1.0 * x[0] - 1.0 * x[2] + 6.0 * x[3], "c1")
然后，我们调用 mindoptpy.MdoModel.set_quadratic_elements() 来设置目标的二次项系数 \(Q\)。前两组输入向量分别表示二次项中所有非零项的两个变量的索引，最后一组输入向量是与之相对应的非零系数值。
Note
为了确保 \(Q\) 的对称性，用户只需要输入其下三角形部分，并且在求解器内部会乘以 1/2.
52 # Add quadratic objective matrix Q.
53 #
54 # Note.
55 # 1. The objective function is defined as c^Tx + 1/2 x^TQx, where Q is stored with coordinate format.
56 # 2. Q will be scaled by 1/2 internally.
57 # 3. To ensure the symmetricity of Q, user needs to input only the lower triangular part.
58 #
59 # Q = [ 1.0 0.5 0 0 ]
60 # [ 0.5 1.0 0 0 ]
61 # [ 0.0 0.0 1.0 0 ]
62 # [ 0 0 0 1.0 ]
63 model.set_quadratic_elements([ x[0], x[1], x[1], x[2], x[3] ], [ x[0], x[0], x[1], x[2], x[3] ], [ 1.0, 0.5, 1.0, 1.0, 1.0 ])
问题输入完成后，再调用 mindoptpy.MdoModel.solve_prob() 求解优化问题，并用 mindoptpy.MdoModel.display_results() 来查看优化结果：
65 # Step 3. Solve the problem and populate the result.
66 model.solve_prob()
67 model.display_results()
最后，我们调用 mindoptpy.MdoModel.free_mdl() 来释放内存：
78 model.free_mdl()
文件链接 mdo_qo_ex1.py 提供了完整源代码：
1"""
2/**
3 * Description
4 * -----------
5 *
6 * Quadratuc optimization (row-wise input).
7 *
8 * Formulation
9 * -----------
10 *
11 * Minimize
12 * obj: 1 x0 + 1 x1 + 1 x2 + 1 x3
13 * + 1/2 [ x0^2 + x1^2 + x2^2 + x3^2 + x0 x1]
14 * Subject To
15 * c1 : 1 x0 + 1 x1 + 2 x2 + 3 x3 >= 1
16 * c2 : 1 x0 - 1 x2 + 6 x3 = 1
17 * Bounds
18 * 0 <= x0 <= 10
19 * 0 <= x1
20 * 0 <= x2
21 * 0 <= x3
22 * End
23 */
24"""
25from mindoptpy import *
26
27
28if __name__ == "__main__":
29
30 MDO_INFINITY = MdoModel.get_infinity()
31
32 # Step 1. Create a model and change the parameters.
33 model = MdoModel()
34
35 try:
36 # Step 2. Input model.
37 # Change to minimization problem.
38 model.set_int_attr(MDO_INT_ATTR.MIN_SENSE, 1)
39
40 # Add variables.
41 x = []
42 x.append(model.add_var(0.0, 10.0, 1.0, None, "x0", False))
43 x.append(model.add_var(0.0, MDO_INFINITY, 1.0, None, "x1", False))
44 x.append(model.add_var(0.0, MDO_INFINITY, 1.0, None, "x2", False))
45 x.append(model.add_var(0.0, MDO_INFINITY, 1.0, None, "x3", False))
46
47 # Add constraints.
48 # Note that the nonzero elements are inputted in a row-wise order here.
49 model.add_cons(1.0, MDO_INFINITY, 1.0 * x[0] + 1.0 * x[1] + 2.0 * x[2] + 3.0 * x[3], "c0")
50 model.add_cons(1.0, 1.0, 1.0 * x[0] - 1.0 * x[2] + 6.0 * x[3], "c1")
51
52 # Add quadratic objective matrix Q.
53 #
54 # Note.
55 # 1. The objective function is defined as c^Tx + 1/2 x^TQx, where Q is stored with coordinate format.
56 # 2. Q will be scaled by 1/2 internally.
57 # 3. To ensure the symmetricity of Q, user needs to input only the lower triangular part.
58 #
59 # Q = [ 1.0 0.5 0 0 ]
60 # [ 0.5 1.0 0 0 ]
61 # [ 0.0 0.0 1.0 0 ]
62 # [ 0 0 0 1.0 ]
63 model.set_quadratic_elements([ x[0], x[1], x[1], x[2], x[3] ], [ x[0], x[0], x[1], x[2], x[3] ], [ 1.0, 0.5, 1.0, 1.0, 1.0 ])
64
65 # Step 3. Solve the problem and populate the result.
66 model.solve_prob()
67 model.display_results()
68
69 except MdoError as e:
70 print("Received Mindopt exception.")
71 print(" - Code : {}".format(e.code))
72 print(" - Reason : {}".format(e.message))
73 except Exception as e:
74 print("Received exception.")
75 print(" - Reason : {}".format(e))
76 finally:
77 # Step 4. Free the model.
78 model.free_mdl()