1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
|
/* -------------------------------------------------------------------------- *
* Simbody(tm): SimTKmath *
* -------------------------------------------------------------------------- *
* This is part of the SimTK biosimulation toolkit originating from *
* Simbios, the NIH National Center for Physics-Based Simulation of *
* Biological Structures at Stanford, funded under the NIH Roadmap for *
* Medical Research, grant U54 GM072970. See https://simtk.org/home/simbody. *
* *
* Portions copyright (c) 2007-12 Stanford University and the Authors. *
* Authors: Jack Middleton *
* Contributors: *
* *
* Licensed under the Apache License, Version 2.0 (the "License"); you may *
* not use this file except in compliance with the License. You may obtain a *
* copy of the License at http://www.apache.org/licenses/LICENSE-2.0. *
* *
* Unless required by applicable law or agreed to in writing, software *
* distributed under the License is distributed on an "AS IS" BASIS, *
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
* See the License for the specific language governing permissions and *
* limitations under the License. *
* -------------------------------------------------------------------------- */
#include "SimTKmath.h"
#include <iostream>
using namespace SimTK;
static int NUMBER_OF_PARAMETERS = 2;
static int NUMBER_OF_EQUALITY_CONSTRAINTS = 0;
static int NUMBER_OF_INEQUALITY_CONSTRAINTS = 2;
/*
*
* Problem statement:
*
* minimize: (x1+5)^2 + (x2 - 4)^2
*
* s.t. x1 - x2^2 <= 0 // inequality constraint
x1 + x2 >= -2 // inequality constraint
*
* Starting point:
* x = ( 5, 5) will be used for the initial conditions
*
* Optimal solution:
* x = (1.00000000 )
*
*/
class ProblemSystem : public OptimizerSystem {
public:
int objectiveFunc( const Vector &coefficients, bool new_coefficients, Real& f ) const override {
const Real *x;
x = &coefficients[0];
f = (x[0] - 5.0)*(x[0] - 5.0) + (x[1] - 1.0)*(x[1] - 1.0);
return( 0 );
}
int gradientFunc( const Vector &coefficients, bool new_coefficients, Vector &gradient ) const override{
const Real *x;
x = &coefficients[0];
gradient[0] = 2.0*(x[0] - 5.0);
gradient[1] = 2.0*(x[1] - 1.0);
return(0);
}
/*
** Method to compute the value of the constraints.
** Equality constraints are first followed by the any inequality constraints
*/
int constraintFunc( const Vector &coefficients, bool new_coefficients, Vector &constraints) const override{
const Real *x;
x = &coefficients[0];
constraints[0] = x[0] - x[1]*x[1];
constraints[1] = x[1] - x[0] + 2.0;
return(0);
}
/*
** Method to compute the jacobian of the constraints.
**
*/
int constraintJacobian( const Vector& coefficients, bool new_coefficients, Matrix& jac) const override{
const Real *x;
x = &coefficients[0];
jac(0,0) = 1.0;
jac(0,1) = -2.0*x[1];
jac(1,0) = -1.0;
jac(1,1) = 1.0;
return(0);
}
ProblemSystem( const int numParams, const int numEqualityConstraints, const int numInequalityConstraints ) :
OptimizerSystem( numParams )
{
setNumEqualityConstraints( numEqualityConstraints );
setNumInequalityConstraints( numInequalityConstraints );
}
};
int main() {
/* create the system to be optimized */
ProblemSystem sys(NUMBER_OF_PARAMETERS, NUMBER_OF_EQUALITY_CONSTRAINTS, NUMBER_OF_INEQUALITY_CONSTRAINTS);
Vector results(NUMBER_OF_PARAMETERS);
/* set initial conditions */
results[0] = 5.0;
results[1] = 5.0;
Real f = NaN;
try {
Optimizer opt( sys );
opt.setConvergenceTolerance( .0000001 );
/* compute optimization */
f = opt.optimize( results );
}
catch (const std::exception& e) {
std::cout << "ConstrainedOptimization.cpp Caught exception:" << std::endl;
std::cout << e.what() << std::endl;
}
printf("Optimal Solution: f = %f parameters = %f %f \n",f,results[0],results[1]);
return 0;
}
|
