5.3.4. QP modeling and optimization in Python¶
This topic describes how to use the Python API of MindOpt to build a model and solve the problem in Examples of quadratic programming problems.
5.3.4.1. Input by row: mdo_qo_ex1¶
Load the Python package.
25from mindoptpy import *
Create an optimization model.
32 # Step 1. Create a model and change the parameters.
33 model = MdoModel()
Call mindoptpy.MdoModel.set_int_attr() to set the target function to Minimization, call mindoptpy.MdoModel.add_var() to add four optimization variables, and define the upper bound, lower bound, names, and types of the variables. For more information about how to use mindoptpy.MdoModel.set_int_attr() and mindoptpy.MdoModel.add_var(), see Python API.
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))
Add linear constraints.
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")
Call mindoptpy.MdoModel.set_quadratic_elements() to set the quadratic coefficient \(Q\) for the object. The former two groups of vectors indicate the indexes of the two variables of all non-zero elements in the quadratic term, respectively, and the last group of vectors indicate the corresponding non-zero coefficient values.
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.
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 ])
Call mindoptpy.MdoModel.solve_prob() to solve the optimization problem, and call mindoptpy.MdoModel.display_results() to view the optimization result.
65 # Step 3. Solve the problem and populate the result.
66 model.solve_prob()
67 model.display_results()
Call mindoptpy.MdoModel.free_mdl() to release the memory.
78 model.free_mdl()
The linked file mdo_qo_ex1.py provides complete source code:
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()