5.3.2. C 语言的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。
5.3.2.1. 按行输入：MdoQoEx1¶
首先，引入头文件：
24#include "Mindopt.h"
并创建优化模型：
87 /*------------------------------------------------------------------*/
88 /* Step 1. Create a model and change the parameters. */
89 /*------------------------------------------------------------------*/
90 /* Create an empty model. */
91 MDO_CHECK_CALL(Mdo_createMdl(&model));
接下来，我们通过 Mdo_setIntAttr() 将目标函数设置为 最小化 ，并调用 Mdo_addCol() 来添加四个优化变量，定义其下界、上界、名称和类型（关于 Mdo_setIntAttr() 和 Mdo_addCol() 的详细使用方式，请参考 C 接口函数）：
93 /*------------------------------------------------------------------*/
94 /* Step 2. Input model. */
95 /*------------------------------------------------------------------*/
96 /* Change to minimization problem. */
97 MDO_CHECK_CALL(Mdo_setIntAttr(model, MDO_INT_ATTR_MIN_SENSE, MDO_YES));
98
99 /* Add variables. */
100 MDO_CHECK_CALL(Mdo_addCol(model, 0.0, 10.0, 1.0, 0, NULL, NULL, "x0", MDO_NO));
101 MDO_CHECK_CALL(Mdo_addCol(model, 0.0, MDO_INFINITY, 1.0, 0, NULL, NULL, "x1", MDO_NO));
102 MDO_CHECK_CALL(Mdo_addCol(model, 0.0, MDO_INFINITY, 1.0, 0, NULL, NULL, "x2", MDO_NO));
103 MDO_CHECK_CALL(Mdo_addCol(model, 0.0, MDO_INFINITY, 1.0, 0, NULL, NULL, "x3", MDO_NO));
Note
矩阵的非零元将在后面按 列 输入；因此，Mdo_addCol() 中，按 列 输入非零元的相关参数 size 、 indices 、 value 分别用 0 、 NULL 、 NULL 代替（换句话说，此时问题无约束）。
以下我们将开始添加线性约束中的的非零元及其上下界，我们使用以下四列数组来定义线性约束；其中， row1_idx 和 row2_idx 分别表示第一和第二个约束中非零元素的位置（索引），而 row1_val 和 row2_val 则是与之相对应的非零数值。
48 const int row1_idx[] = { 0, 1, 2, 3 };
49 const double row1_val[] = { 1.0, 1.0, 2.0, 3.0 };
50 const int row2_idx[] = { 0, 2, 3 };
51 const double row2_val[] = { 1.0, -1.0, 6.0 };
我们调用 Mdo_addRow() 来输入约束：
105 /* Add constraints.
106 * Note that the nonzero elements are inputted in a row-wise order here.
107 */
108 MDO_CHECK_CALL(Mdo_addRow(model, 1.0, MDO_INFINITY, 4, row1_idx, row1_val, "c0"));
109 MDO_CHECK_CALL(Mdo_addRow(model, 1.0, 1.0, 3, row2_idx, row2_val, "c1"));
接下来我们将添加二次规划中的目标函数的二次项系数 \(Q\)。我们使用以下3个参数来定义：其中 qo_col1 和 qo_col2 分别记录二次项中所有非零项的两个变量索引，而 qo_values 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.
53 /* Quadratic objective matrix Q.
54 *
55 * Note.
56 * 1. The objective function is defined as c^Tx + 1/2 x^TQx, where Q is stored with coordinate format.
57 * 2. Q will be scaled by 1/2 internally.
58 * 3. To ensure the symmetricity of Q, user needs to input only the lower triangular part.
59 *
60 * Q = [ 1.0 0.5 0 0 ]
61 * [ 0.5 1.0 0 0 ]
62 * [ 0.0 0.0 1.0 0 ]
63 * [ 0 0 0 1.0 ]
64 */
65 const int qo_col1[] =
66 {
67 0,
68 1, 1,
69 2,
70 3
71 };
72 const int qo_col2[] =
73 {
74 0,
75 0, 1,
76 2,
77 3
78 };
79 const double qo_values[] =
80 {
81 1.0,
82 0.5, 1.0,
83 1.0,
84 1.0
85 };
我们调用 Mdo_setQuadraticElements() 设置目标的二次项：
112 /* Add quadratic objective term. */
113 MDO_CHECK_CALL(Mdo_setQuadraticElements(model, 5, qo_col1, qo_col2, qo_values));
问题输入完成后，再调用 Mdo_solveProb() 求解优化问题，并通过 Mdo_displayResults() 查看优化结果：
114 /*------------------------------------------------------------------*/
115 /* Step 3. Solve the problem and populate the result. */
116 /*------------------------------------------------------------------*/
117 /* Solve the problem. */
118 MDO_CHECK_CALL(Mdo_solveProb(model));
119 Mdo_displayResults(model);
最后，调用 Mdo_freeMdl() 来释放内存：
121 /*------------------------------------------------------------------*/
122 /* Step 4. Free the model. */
123 /*------------------------------------------------------------------*/
124 /* Free the model. */
125 Mdo_freeMdl(&model);
文件链接 MdoQoEx1.c 提供了完整源代码：
1/**
2 * Description
3 * -----------
4 *
5 * Quadratic 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 <stdio.h>
24#include "Mindopt.h"
25
26/* Macro to check the return code */
27#define MDO_CHECK_CALL(MDO_CALL) \
28 code = MDO_CALL; \
29 if (code != MDO_OKAY) \
30 { \
31 Mdo_explainResult(model, code, str); \
32 Mdo_freeMdl(&model); \
33 fprintf(stderr, "===================================\n"); \
34 fprintf(stderr, "Error : code <%d>\n", code); \
35 fprintf(stderr, "Reason : %s\n", str); \
36 fprintf(stderr, "===================================\n"); \
37 return (int)code; \
38 }
39
40int main(void)
41{
42 /* Variables. */
43 char str[1024] = { "\0" };
44 MdoMdl * model = NULL;
45 MdoResult code = MDO_OKAY;
46 MdoStatus status = MDO_UNKNOWN;
47
48 const int row1_idx[] = { 0, 1, 2, 3 };
49 const double row1_val[] = { 1.0, 1.0, 2.0, 3.0 };
50 const int row2_idx[] = { 0, 2, 3 };
51 const double row2_val[] = { 1.0, -1.0, 6.0 };
52
53 /* Quadratic objective matrix Q.
54 *
55 * Note.
56 * 1. The objective function is defined as c^Tx + 1/2 x^TQx, where Q is stored with coordinate format.
57 * 2. Q will be scaled by 1/2 internally.
58 * 3. To ensure the symmetricity of Q, user needs to input only the lower triangular part.
59 *
60 * Q = [ 1.0 0.5 0 0 ]
61 * [ 0.5 1.0 0 0 ]
62 * [ 0.0 0.0 1.0 0 ]
63 * [ 0 0 0 1.0 ]
64 */
65 const int qo_col1[] =
66 {
67 0,
68 1, 1,
69 2,
70 3
71 };
72 const int qo_col2[] =
73 {
74 0,
75 0, 1,
76 2,
77 3
78 };
79 const double qo_values[] =
80 {
81 1.0,
82 0.5, 1.0,
83 1.0,
84 1.0
85 };
86
87 /*------------------------------------------------------------------*/
88 /* Step 1. Create a model and change the parameters. */
89 /*------------------------------------------------------------------*/
90 /* Create an empty model. */
91 MDO_CHECK_CALL(Mdo_createMdl(&model));
92
93 /*------------------------------------------------------------------*/
94 /* Step 2. Input model. */
95 /*------------------------------------------------------------------*/
96 /* Change to minimization problem. */
97 MDO_CHECK_CALL(Mdo_setIntAttr(model, MDO_INT_ATTR_MIN_SENSE, MDO_YES));
98
99 /* Add variables. */
100 MDO_CHECK_CALL(Mdo_addCol(model, 0.0, 10.0, 1.0, 0, NULL, NULL, "x0", MDO_NO));
101 MDO_CHECK_CALL(Mdo_addCol(model, 0.0, MDO_INFINITY, 1.0, 0, NULL, NULL, "x1", MDO_NO));
102 MDO_CHECK_CALL(Mdo_addCol(model, 0.0, MDO_INFINITY, 1.0, 0, NULL, NULL, "x2", MDO_NO));
103 MDO_CHECK_CALL(Mdo_addCol(model, 0.0, MDO_INFINITY, 1.0, 0, NULL, NULL, "x3", MDO_NO));
104
105 /* Add constraints.
106 * Note that the nonzero elements are inputted in a row-wise order here.
107 */
108 MDO_CHECK_CALL(Mdo_addRow(model, 1.0, MDO_INFINITY, 4, row1_idx, row1_val, "c0"));
109 MDO_CHECK_CALL(Mdo_addRow(model, 1.0, 1.0, 3, row2_idx, row2_val, "c1"));
110
111 /* Add quadratic objective term. */
112 MDO_CHECK_CALL(Mdo_setQuadraticElements(model, 5, qo_col1, qo_col2, qo_values));
113
114 /*------------------------------------------------------------------*/
115 /* Step 3. Solve the problem and populate the result. */
116 /*------------------------------------------------------------------*/
117 /* Solve the problem. */
118 MDO_CHECK_CALL(Mdo_solveProb(model));
119 Mdo_displayResults(model);
120
121 /*------------------------------------------------------------------*/
122 /* Step 4. Free the model. */
123 /*------------------------------------------------------------------*/
124 /* Free the model. */
125 Mdo_freeMdl(&model);
126
127 return (int)code;
128}