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/* -------------------------------------------------------------------------- *
* Simbody(tm) Example: Constrained Optimization w/Analytical Gradient *
* -------------------------------------------------------------------------- *
* 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) 2006-12 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 NumberOfParameters = 4;
static int NumberOfEqualityConstraints = 1;
static int NumberOfInequalityConstraints = 1;
/*
* This example was adapted from IPOPT's hs071 example
*
* Problem statement:
*
* minimize: x1*x4*(x1 + x2 + x3) + x3
*
* s.t. x1*x2*x3*x4 >= 25 inequality constraint
* x1**2 + x2**2 + x3**2 + x4**2 - 40.0 = 0.0 equality constraint
*
* 1 <= x1,x2,x3,x4 <= 5 each parameter has a lower limit of 1.0 and an upper limit of 5.0
*
* Starting point:
* x = (1, 5, 5, 1) will be used for the initial conditions
*
* Optimal solution:
* x = (1.00000000, 4.74299963, 3.82114998, 1.37940829)
*
*/
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] * x[3] * (x[0] + x[1] + x[2]) + x[2];
return( 0 );
}
int gradientFunc( const Vector &coefficients, bool new_coefficients, Vector &gradient ) const override{
const Real *x;
x = &coefficients[0];
gradient[0] = x[0] * x[3] + x[3] * (x[0] + x[1] + x[2]);
gradient[1] = x[0] * x[3];
gradient[2] = x[0] * x[3] + 1;
gradient[3] = x[0] * (x[0] + x[1] + x[2]);
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[0] + x[1]*x[1] + x[2]*x[2] + x[3]*x[3] - 40.0;
constraints[1] = x[0] * x[1] * x[2] * x[3] - 25.0;
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) = 2*x[0];
jac(0,1) = 2*x[1];
jac(0,2) = 2*x[2];
jac(0,3) = 2*x[3];
jac(1,0) = x[1]*x[2]*x[3];
jac(1,1) = x[0]*x[2]*x[3];
jac(1,2) = x[0]*x[1]*x[3];
jac(1,3) = x[0]*x[1]*x[2];
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(NumberOfParameters, NumberOfEqualityConstraints, NumberOfInequalityConstraints);
Vector results(NumberOfParameters);
Vector lower_bounds(NumberOfParameters);
Vector upper_bounds(NumberOfParameters);
/* set initial conditions */
results[0] = 1.0;
results[1] = 5.0;
results[2] = 5.0;
results[3] = 1.0;
/* set bounds */
for(int i=0;i<NumberOfParameters;i++) {
lower_bounds[i] = 1.0;
upper_bounds[i] = 5.0;
}
sys.setParameterLimits( lower_bounds, upper_bounds );
Real f = NaN;
try {
Optimizer opt( sys );
opt.setConvergenceTolerance( .0001 );
/* 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 %f %f \n",f,results[0],results[1],results[2],results[3]);
return 0;
}
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