ipopt CppAD 非线性规划

一. 参考

• 无人车系统（十）：c++与python非线性规(优)划（化）工具
• ipopt 安装参考我这里面的：MPC (c++) 和 udacity模拟器仿真

二. 使用

1. CMakeLists 文件

project(ipopt_test)

cmake_minimum_required (VERSION 3.5)

# -g allows for gdb debugging
# turn on -03 for best performance
add_definitions(-std=c++11 -O3)

set(CXX_FLAGS "-Wall")
set(CMAKE_CXX_FLAGS, "${CXX_FLAGS}")

set(sources src/main.cpp)

include_directories(/usr/local/include)
link_directories(/usr/local/lib)
include_directories(src/Eigen-3.3)

add_executable(ipopt_test ${sources})

target_link_libraries(ipopt_test ipopt)

2. 代码

#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
          AD<double> x1 = x[0];
          AD<double> x2 = x[1];
          AD<double> x3 = x[2];
          AD<double> x4 = x[3];
          // f(x) objective function
          fg[0] = x1 * x4 * (x1 + x2 + x3) + x3;
          // constraints
          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

    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;
    }

    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";


    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
    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;
}

• 结果：

CppAD : Hello World Demo!
solution: {
    
     1, 4.743, 3.82115, 1.37941 }
CppAD res:1