5.3.3. C++ 的QP建模和优化¶
在本节中，我们将使用 MindOpt C++ 语言的 API 来建模以及求解 二次规划问题示例 中的问题。
5.3.3.1. 按行输入：MdoQoEx1¶
首先，引入头文件：
25#include "MindoptCpp.h"
并创建优化模型：
31 /*------------------------------------------------------------------*/
32 /* Step 1. Create a model and change the parameters. */
33 /*------------------------------------------------------------------*/
34 /* Create an empty model. */
35 MdoModel model;
接下来，我们通过 mindopt::MdoModel::setIntAttr() 将目标函数设置为 最小化 ，并调用 mindopt::MdoModel::addVar() 来添加四个优化变量，定义其下界、上界、名称和类型（有关 mindopt::MdoModel::setIntAttr() 和 mindopt::MdoModel::addVar() 的详细使用方式，请参考 C++ 接口函数）：
39 /*------------------------------------------------------------------*/
40 /* Step 2. Input model. */
41 /*------------------------------------------------------------------*/
42 /* Change to minimization problem. */
43 model.setIntAttr(MDO_INT_ATTR::MIN_SENSE, MDO_YES);
44
45 /* Add variables. */
46 std::vector<MdoVar> x;
47 x.push_back(model.addVar(0.0, 10.0, 1.0, "x0", MDO_NO));
48 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, "x1", MDO_NO));
49 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, "x2", MDO_NO));
50 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, "x3", MDO_NO));
接着，我们开始添加线性约束：
53 model.addCons(1.0, MDO_INFINITY, 1.0 * x[0] + 1.0 * x[1] + 2.0 * x[2] + 3.0 * x[3], "c0");
54 model.addCons(1.0, 1.0, 1.0 * x[0] - 1.0 * x[2] + 6.0 * x[3], "c1");
然后，我们调用 mindopt::MdoModel::setQuadraticElements() 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.
56 /* Add quadratic objective matrix Q.
57 *
58 * Note.
59 * 1. The objective function is defined as c^Tx + 1/2 x^TQx, where Q is stored with coordinate format.
60 * 2. Q will be scaled by 1/2 internally.
61 * 3. To ensure the symmetricity of Q, user needs to input only the lower triangular part.
62 *
63 * Q = [ 1.0 0.5 0 0 ]
64 * [ 0.5 1.0 0 0 ]
65 * [ 0.0 0.0 1.0 0 ]
66 * [ 0 0 0 1.0 ]
67 */
68 model.setQuadraticElements
69 (
70 { x[0], x[1], x[1], x[2], x[3] },
71 { x[0], x[0], x[1], x[2], x[3] },
72 { 1.0, 0.5, 1.0, 1.0, 1.0 }
73 );
问题输入完成后，再调用 mindopt::MdoModel::solveProb() 求解优化问题，并通过 mindopt::MdoModel::displayResults() 查看优化结果：
75 /*------------------------------------------------------------------*/
76 /* Step 3. Solve the problem and populate the result. */
77 /*------------------------------------------------------------------*/
78 /* Solve the problem. */
79 model.solveProb();
80 model.displayResults();
文件链接 MdoQoEx1.cpp 提供了完整源代码：
1/**
2 * Description
3 * -----------
4 *
5 * Linear optimization (row-wise input).
6 *
7 * Formulation
8 * -----------
9 *
10 * Minimize
11 * obj: 1 x0 + 1 x1 + 1 x2 + 1 x3
12 * + 1/2 [ x0^2 + x1^2 + x2^2 + x3^2 + x0 x1]
13 * Subject To
14 * c0 : 1 x0 + 1 x1 + 2 x2 + 3 x3 >= 1
15 * c1 : 1 x0 - 1 x2 + 6 x3 = 1
16 * Bounds
17 * 0 <= x0 <= 10
18 * 0 <= x1
19 * 0 <= x2
20 * 0 <= x3
21 * End
22 */
23#include <iostream>
24#include <vector>
25#include "MindoptCpp.h"
26
27using namespace mindopt;
28
29int main(void)
30{
31 /*------------------------------------------------------------------*/
32 /* Step 1. Create a model and change the parameters. */
33 /*------------------------------------------------------------------*/
34 /* Create an empty model. */
35 MdoModel model;
36
37 try
38 {
39 /*------------------------------------------------------------------*/
40 /* Step 2. Input model. */
41 /*------------------------------------------------------------------*/
42 /* Change to minimization problem. */
43 model.setIntAttr(MDO_INT_ATTR::MIN_SENSE, MDO_YES);
44
45 /* Add variables. */
46 std::vector<MdoVar> x;
47 x.push_back(model.addVar(0.0, 10.0, 1.0, "x0", MDO_NO));
48 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, "x1", MDO_NO));
49 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, "x2", MDO_NO));
50 x.push_back(model.addVar(0.0, MDO_INFINITY, 1.0, "x3", MDO_NO));
51
52 /* Add constraints. */
53 model.addCons(1.0, MDO_INFINITY, 1.0 * x[0] + 1.0 * x[1] + 2.0 * x[2] + 3.0 * x[3], "c0");
54 model.addCons(1.0, 1.0, 1.0 * x[0] - 1.0 * x[2] + 6.0 * x[3], "c1");
55
56 /* Add quadratic objective matrix Q.
57 *
58 * Note.
59 * 1. The objective function is defined as c^Tx + 1/2 x^TQx, where Q is stored with coordinate format.
60 * 2. Q will be scaled by 1/2 internally.
61 * 3. To ensure the symmetricity of Q, user needs to input only the lower triangular part.
62 *
63 * Q = [ 1.0 0.5 0 0 ]
64 * [ 0.5 1.0 0 0 ]
65 * [ 0.0 0.0 1.0 0 ]
66 * [ 0 0 0 1.0 ]
67 */
68 model.setQuadraticElements
69 (
70 { x[0], x[1], x[1], x[2], x[3] },
71 { x[0], x[0], x[1], x[2], x[3] },
72 { 1.0, 0.5, 1.0, 1.0, 1.0 }
73 );
74
75 /*------------------------------------------------------------------*/
76 /* Step 3. Solve the problem and populate the result. */
77 /*------------------------------------------------------------------*/
78 /* Solve the problem. */
79 model.solveProb();
80 model.displayResults();
81 }
82 catch (MdoException & e)
83 {
84 std::cerr << "===================================" << std::endl;
85 std::cerr << "Error : code <" << e.getResult() << ">" << std::endl;
86 std::cerr << "Reason : " << model.explainResult(e.getResult()) << std::endl;
87 std::cerr << "===================================" << std::endl;
88
89 return static_cast<int>(e.getResult());
90 }
91
92 return static_cast<int>(MDO_OKAY);
93}