5.3.2. QP modeling and optimization in C¶
This topic describes how to use the C API of MindOpt to build a model and solve the problem in Examples of quadratic programming problems.
5.3.2.1. Input by row: MdoQoEx1¶
Load the header file.
24#include "Mindopt.h"
Create an optimization model.
87 /*------------------------------------------------------------------*/
88 /* Step 1. Create a model and change the parameters. */
89 /*------------------------------------------------------------------*/
90 /* Create an empty model. */
91 MDO_CHECK_CALL(Mdo_createMdl(&model));
Call Mdo_setIntAttr() to set the target function to Minimization, call Mdo_addCol() to add four optimization variables, and define the upper and lower bounds, names, and types of the variables. For more information about how to use Mdo_setIntAttr() and Mdo_addCol(), see C API.
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
The non-zero elements in the matrix will be input by column later. Therefore, in Mdo_addCol(), replace the size , indices , and value parameters of non-zero elements that are input by column with 0, NULL, and NULL, respectively. In other words, the problem has no constraints for the moment.
Now, add non-zero elements and their upper and lower bounds of linear constraints. Use the following four arrays to define linear constraints. row1_idx and row2_idx indicate the position (index) for a non-zero element in the first and second constraints, respectively, and row1_val and row2_val are the non-zero values of these elements.
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 };
Call Mdo_addRow() to input the constraints.
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"));
Add the quadratic coefficient \(Q\) of the target function in quadratic programming. Three parameters are used. qo_col1 and qo_col2 record the two variable indexes of all non-zero elements in the quadratic term, respectively, and qo_values is the corresponding non-zero coefficient value.
Note
To ensure the symmetry of \(Q\), you only need to input the triangle part, which will be multiplied by 1/2 inside the solver.
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 };
Call Mdo_setQuadraticElements() to set the quadratic term of the object.
112 /* Add quadratic objective term. */
113 MDO_CHECK_CALL(Mdo_setQuadraticElements(model, 5, qo_col1, qo_col2, qo_values));
Call Mdo_solveProb() to solve the optimization problem and call Mdo_displayResults() to view the optimization result.
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);
Call Mdo_freeMdl() to release the memory.
121 /*------------------------------------------------------------------*/
122 /* Step 4. Free the model. */
123 /*------------------------------------------------------------------*/
124 /* Free the model. */
125 Mdo_freeMdl(&model);
The linked file MdoQoEx1.c provides complete source code:
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}