目录
1、IPOPT的安装（简洁版本）
2、IPOPT测试案例
3、ADOL-C的使用
4、CppAD的使用
5、IPOPT的initial gauss 以及 warm star
参考链接：
优化，在Apollo规划模块中占据了重要的地位
Apollo中 OSQP 和 IPOPT 的应用：
OSQP | IPOPT |
参考线：discrete_points_smoother（ FemPosSmooth） 参考线：qp_spline_smoother | 参考线：spiral_smoother 分段五次螺旋线非线性优化拟合 参考线：discrete_points_smoother（CosThetaSmooth） ipopt+adol-c |
Lattice中横向规划中使用的基于二次规划的轨迹规划 | Hybrid A*的轨迹优化 |
路径规划的QP 速度规划中DP之后的QP | 速度规划中DP之后的IPOPT |
其中OSQP在之前的文章中测试过，这篇文章主要进行IPOPT的相关实践
非线性优化的一般形式为：
IPOPT是一种常用的非线性优化求解器，使用内点法进行求解
对于复杂问题，需要借助自动微分工具，帮助求解梯度、Yacobian矩阵、Hessian矩阵，
如ADOL-C，CppAD
1、IPOPT的安装（简洁版本）
(1).安装apt包
sudo apt-get install gcc g++ gfortran git patch wget pkg-config liblapack-dev libmetis-dev(2).安装BLAS and LAPACK
即为前面apt安装的liblapack-dev
(3).安装HSL 官网注册申请下载
需要教育网邮箱申请，
同时下载如下库.并将前面下载的HSL包解压后改名为coinhsl(例如coinhsl-archive-2021.05.05 => coinhsl)后复制到ThirdParty-HSL文件夹中,最后进行编译安装.
git clone https://github.com/coin-or-tools/ThirdParty-HSL.git
cd ThirdParty-HSL
./configure
make
sudo make install
sudo ldconfig(4).安装IPOPT
mkdir build
cd build
sudo ../configure --prefix=/usr/local/ #安装到指定位置
sudo make
sudo make test
sudo make installmake test的输出应该如下：
Running unitTests...
Testing AMPL Solver Executable...
Test passed!
Testing C++ Example...
Test passed!
Testing C Example...
Test passed!
Testing Fortran Example...
Test passed!
Skip testing Java Example (Java interface not build)
Testing sIpopt Example parametric_cpp...
Test passed!
Testing sIpopt Example redhess_cpp...
Test passed!
Testing EmptyNLP Example...
Test passed!
Testing GetCurr Example...
Test passed!(5).安装成功与否
进入IPOPT源码文件夹如下位置,用官方例子测试
cd Ipopt-releases-3.14.2/build/examples/Cpp_example
sudo make
./solver2、IPOPT测试案例
#include "IpIpoptApplication.hpp"
#include "IpSolveStatistics.hpp"
#include "MyNLP.hpp"
#include <iostream>
using namespace Ipopt;
int main(int argv, char* argc[])
{
// Create an instance of your nlp...
SmartPtr<TNLP> mynlp = new MyNLP();
// Create an instance of the IpoptApplication
//
// We are using the factory, since this allows us to compile this
// example with an Ipopt Windows DLL
SmartPtr<IpoptApplication> app = IpoptApplicationFactory();
// Initialize the IpoptApplication and process the options
ApplicationReturnStatus status;
status = app->Initialize();
if (status != Solve_Succeeded) {
std::cout << std::endl << std::endl << "*** Error during initialization!" << std::endl;
return (int) status;
}
status = app->OptimizeTNLP(mynlp);
if (status == Solve_Succeeded) {
// Retrieve some statistics about the solve
Index iter_count = app->Statistics()->IterationCount();
std::cout << std::endl << std::endl << "*** The problem solved in " << iter_count << " iterations!" << std::endl;
Number final_obj = app->Statistics()->FinalObjective();
std::cout << std::endl << std::endl << "*** The final value of the objective function is " << final_obj << '.' << std::endl;
}
return (int) status;
}
3、ADOL-C的使用
待补充
4、CppAD的使用
#include <iostream>
#include <cppad/ipopt/solve.hpp>
using namespace std;
namespace {
using CppAD::AD;
class FG_eval {
public:
typedef CPPAD_TESTVECTOR(AD<double>) ADvector;
//
void operator()(ADvector& fg, const ADvector& x)
{
assert(fg.size() == 3);
assert(x.size() == 4);
// variables 优化变量
AD<double> x1 = x[0];
AD<double> x2 = x[1];
AD<double> x3 = x[2];
AD<double> x4 = x[3];
// f(x) objective function 目标函数
fg[0] = x1 * x4 * (x1 + x2 + x3) + x3;
// constraints 约束条件
fg[1] = x1 * x2 * x3 * x4;
fg[2] = x1 * x1 + x2 * x2 + x3 * x3 + x4 * x4;
return;
}
};
} //end namespace
bool get_started(void)
{
bool ok = true;
size_t i;
typedef CPPAD_TESTVECTOR(double) Dvector;
size_t nx = 4; // number of varibles
size_t ng = 2; // number of constraints
Dvector x0(nx); // initial condition of varibles 初始？
x0[0] = 1.0;
x0[1] = 5.0;
x0[2] = 5.0;
x0[3] = 1.0;
// lower and upper bounds for varibles
Dvector xl(nx), xu(nx);
for(i = 0; i < nx; i++)
{
xl[i] = 1.0;
xu[i] = 5.0;
}
//不等式上下界
Dvector gl(ng), gu(ng);
gl[0] = 25.0; gu[0] = 1.0e19;
gl[1] = 40.0; gu[1] = 40.0;
// object that computes objective and constraints
FG_eval fg_eval;
// options
string options;
// turn off any printing
options += "Integer print_level 0\n";
options += "String sb yes\n";
// maximum iterations
options += "Integer max_iter 10\n";
//approximate accuracy in first order necessary conditions;
// see Mathematical Programming, Volume 106, Number 1,
// Pages 25-57, Equation (6)
options += "Numeric tol 1e-6\n";
//derivative tesing
options += "String derivative_test second-order\n";
// maximum amount of random pertubation; e.g.,
// when evaluation finite diff
options += "Numeric point_perturbation_radius 0.\n";
//定义solution并求解
CppAD::ipopt::solve_result<Dvector> solution; // solution
CppAD::ipopt::solve<Dvector, FG_eval>(options, x0, xl, xu, gl, gu, fg_eval, solution); // solve the problem
cout << "solution: " << solution.x << endl;
//check some of the solution values 这个check有什么用？
ok &= solution.status == CppAD::ipopt::solve_result<Dvector>::success;
double check_x[] = {1.000000, 4.743000, 3.82115, 1.379408};
double check_zl[] = {1.087871, 0., 0., 0. };
double check_zu[] = {0., 0., 0., 0. };
double rel_tol = 1e-6; // relative tolerance
double abs_tol = 1e-6; // absolute tolerance
for(i = 0; i < nx; i++)
{
ok &= CppAD::NearEqual(check_x[i], solution.x[i], rel_tol, abs_tol);
ok &= CppAD::NearEqual(check_zl[i], solution.zl[i], rel_tol, abs_tol);
ok &= CppAD::NearEqual(check_zu[i], solution.zu[i], rel_tol, abs_tol);
}
return ok;
}
int main()
{
cout << "CppAD : Hello World Demo!" << endl;
bool res = get_started();
cout << "CppAD res:" << res << endl;
return 0;
}CMakeList.txt
project(ipopt_test)
cmake_minimum_required (VERSION 3.5)
add_definitions(-std=c++11 -O3)
add_executable(ipopt_test main.cpp)
target_link_libraries(ipopt_test ipopt)
5、IPOPT的initial gauss 以及 warm star
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