文章目錄

• • 一. 安裝
  • • 1. ipopt 安裝
    • 2. Casadi 安裝
  • 二. 例子
  • • 1. CmakeLists文件
    • 2. 例子1
    • 3. 例子2
  • 三. github：casadi_test

Casadi 是一款非線性求解器，支持多種語言，官方文檔：casadi/docs

一. 安裝

1. ipopt 安裝

自己寫個sh腳本安裝一下

#!/usr/bin/env bash# Fail on first error. set -ecd "$(dirname "${BASH_SOURCE[0]}")"sudo apt-get install cppad gfortran wget https://www.coin-or.org/download/source/Ipopt/Ipopt-3.12.8.zip -O Ipopt-3.12.8.zip unzip Ipopt-3.12.8.zip# Step by step pushd Ipopt-3.12.8/ThirdParty/Blas ./get.Blas cd ../Lapack ./get.Lapack cd ../Mumps ./get.Mumps cd ../Metis ./get.Metis cd ../ASL ./get.ASLcd .. cd ..mkdir build cd build ../configure make -j4 make install cp -a include/* /usr/include/. cp -a lib/* /usr/lib/. popd# Clean up. cd .. cd .. apt-get clean && rm -rf /var/lib/apt/lists/* rm -rf Ipopt-3.12.8.zip Ipopt-3.12.8

2. Casadi 安裝

#!/usr/bin/env bash# Fail on first error. set -eDIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" && pwd )" echo -e "\033[40;32m${DIR} \033[0m"# download wget https://github.com/casadi/casadi/releases/download/3.5.5/casadi-3.5.5-1.tar.gz tar -zxvf casadi-3.5.5-1.tar.gz echo -e "\033[40;32mdownload finish \033[0m"cd casadi-3.5.5.1 mkdir build && cd build cmake .. -DWITH_IPOPT=ON -DWITH_EXAMPLES=OFF make -j4 sudo make install sudo ldconfig# Clean up. sudo apt-get clean && sudo rm -rf /var/lib/apt/lists/* sudo rm -fr casadi-3.5.5-1.tar.gz casadi-3.5.5.1

舉兩個c++的非線性求解的栗子吧，沒怎么看到過

二. 例子

1. CmakeLists文件

cmake_minimum_required(VERSION 2.8.9)project(casadi_test)set(CMAKE_CXX_STANDARD 11) set(CMAKE_CXX_STANDARD_REQUIRED ON)include_directories(# include${catkin_INCLUDE_DIRS} )add_executable(${PROJECT_NAME}_node src/casadi_test.cpp ) target_link_libraries(${PROJECT_NAME}_node ${catkin_LIBRARIES} casadi)

2. 例子1

#include<iostream> #include<vector> #include <casadi/casadi.hpp>using namespace std; using namespace casadi;int main(int argc, char * argv[] ){cout << "casadi_test" << endl;// This is another way to define a nonlinear solver. Opti is new/** min x1^2 + x2^2 + x3^2* s.t. 6*x1 + 3&x2 + 2*x3 - p0 = 0* p2*x1 + x2 - x3 - 1 = 0* x1, x2, x3 >= 0*/// Optimization variablesSX x = SX::sym("x", 3);std::cout << "x:" << x << std::endl;// ParametersSX p = SX::sym("p", 2);std::cout << "p:" << p << std::endl;// ObjectiveSX f = x(0) * x(0) + x(1) * x(1) + x(2) * x(2);std::cout << "f:" << f << std::endl;// ConstraintsSX g = vertcat(6 * x(0) + 3 * x(1) + 2 * x(2) - p(0), p(1) * x(0) + x(1) - x(2) - 1);std::cout << "g:" << g << std::endl;// Initial guess and bounds for the optimization variablesvector<double> x0 = { 0.15, 0.15, 0.00 };vector<double> lbx = { 0.00, 0.00, 0.00 };vector<double> ubx = { inf, inf, inf };// Nonlinear boundsvector<double> lbg = { 0.00, 0.00 };vector<double> ubg = { 0.00, 0.00 };// Original parameter valuesvector<double> p0 = { 5.00, 1.00 };// NLPSXDict nlp = { { "x", x }, { "p", p }, { "f", f }, { "g", g } };// Create NLP solver and buffersFunction solver = nlpsol("solver", "ipopt", nlp);std::map<std::string, DM> arg, res;// Solve the NLParg["lbx"] = lbx;arg["ubx"] = ubx;arg["lbg"] = lbg;arg["ubg"] = ubg;arg["x0"] = x0;arg["p"] = p0;res = solver(arg);// Print the solutioncout << "--------------------------------" << endl;cout << "Optimal solution for p = " << arg.at("p") << ":" << endl;cout << setw(30) << "Objective: " << res.at("f") << endl;cout << setw(30) << "Primal solution: " << res.at("x") << endl;cout << setw(30) << "Dual solution (x): " << res.at("lam_x") << endl;cout << setw(30) << "Dual solution (g): " << res.at("lam_g") << endl;return 0; }

結(jié)果

djq@djq-UX410UQK:~/test/casadi_test/build$ ./casadi_test_node casadi_test x:[x_0, x_1, x_2] p:[p_0, p_1] f:((sq(x_0)+sq(x_1))+sq(x_2)) g:[((((6*x_0)+(3*x_1))+(2*x_2))-p_0), ((((p_1*x_0)+x_1)-x_2)-1)]****************************************************************************** This program contains Ipopt, a library for large-scale nonlinear optimization.Ipopt is released as open source code under the Eclipse Public License (EPL).For more information visit http://projects.coin-or.org/Ipopt ******************************************************************************This is Ipopt version 3.12.8, running with linear solver mumps. NOTE: Other linear solvers might be more efficient (see Ipopt documentation).Number of nonzeros in equality constraint Jacobian...: 6 Number of nonzeros in inequality constraint Jacobian.: 0 Number of nonzeros in Lagrangian Hessian.............: 3Total number of variables............................: 3variables with only lower bounds: 3variables with lower and upper bounds: 0variables with only upper bounds: 0 Total number of equality constraints.................: 2 Total number of inequality constraints...............: 0inequality constraints with only lower bounds: 0inequality constraints with lower and upper bounds: 0inequality constraints with only upper bounds: 0iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls0 4.5100000e-02 3.63e+00 4.11e-01 -1.0 0.00e+00 - 0.00e+00 0.00e+00 01 5.8681488e-01 8.88e-16 1.95e+00 -1.0 3.91e-01 - 3.37e-01 1.00e+00h 12 5.9327019e-01 8.88e-16 1.00e-06 -1.0 1.32e-02 - 1.00e+00 1.00e+00f 13 5.6004673e-01 0.00e+00 4.92e-02 -2.5 8.93e-02 - 9.26e-01 1.00e+00f 14 5.5264341e-01 1.11e-16 2.83e-08 -2.5 4.42e-02 - 1.00e+00 1.00e+00f 15 5.5114453e-01 2.22e-16 1.50e-09 -3.8 2.36e-02 - 1.00e+00 1.00e+00f 16 5.5102559e-01 8.88e-16 1.50e-09 -3.8 7.16e-03 - 1.00e+00 1.00e+00f 17 5.5102042e-01 8.88e-16 1.84e-11 -5.7 1.77e-03 - 1.00e+00 1.00e+00f 18 5.5102041e-01 8.88e-16 2.51e-14 -8.6 6.77e-05 - 1.00e+00 1.00e+00h 19 5.5102041e-01 0.00e+00 9.06e-15 -9.0 9.29e-08 - 1.00e+00 1.00e+00h 1Number of Iterations....: 9(scaled) (unscaled) Objective...............: 5.5102040816326525e-01 5.5102040816326525e-01 Dual infeasibility......: 9.0609642761140061e-15 9.0609642761140061e-15 Constraint violation....: 0.0000000000000000e+00 0.0000000000000000e+00 Complementarity.........: 9.0911698984221084e-10 9.0911698984221084e-10 Overall NLP error.......: 9.0911698984221084e-10 9.0911698984221084e-10Number of objective function evaluations = 10 Number of objective gradient evaluations = 10 Number of equality constraint evaluations = 10 Number of inequality constraint evaluations = 0 Number of equality constraint Jacobian evaluations = 10 Number of inequality constraint Jacobian evaluations = 0 Number of Lagrangian Hessian evaluations = 9 Total CPU secs in IPOPT (w/o function evaluations) = 0.011 Total CPU secs in NLP function evaluations = 0.001EXIT: Optimal Solution Found.solver : t_proc (avg) t_wall (avg) n_evalnlp_f | 42.00us ( 4.20us) 42.45us ( 4.24us) 10nlp_g | 96.00us ( 9.60us) 88.33us ( 8.83us) 10nlp_grad | 9.00us ( 9.00us) 8.45us ( 8.45us) 1nlp_grad_f | 84.00us ( 7.64us) 79.88us ( 7.26us) 11nlp_hess_l | 52.00us ( 5.78us) 48.97us ( 5.44us) 9nlp_jac_g | 61.00us ( 5.55us) 64.10us ( 5.83us) 11total | 13.08ms ( 13.08ms) 13.08ms ( 13.08ms) 1 -------------------------------- Optimal solution for p = [5, 1]:Objective: 0.55102Primal solution: [0.632653, 0.387755, 0.0204082]Dual solution (x): [-1.43695e-09, -2.3445e-09, -4.45467e-08]Dual solution (g): [-0.163265, -0.285714]

3. 例子2

#include<iostream> #include<vector> #include <casadi/casadi.hpp>using namespace std; using namespace casadi;int main(int argc, char * argv[] ){cout << "casadi_test" << endl;// This is another way to define a nonlinear solver. Opti is new /** min x1*x4*(x1 + x2 + x3) + x3* s.t. x1*x2*x3*x4 >=25x1^2 + x2^2 + x3^2 + x4^2 = 401 <= x1, x2, x3, x4 <= 5 */// Optimization variablesSX x = SX::sym("x", 4);std::cout << "x:" << x << std::endl;// ObjectiveSX f = x(0)*x(3)*(x(0) + x(1) + x(2)) + x(2);// SX f = x(0) * x(0)*x(3) + x(0)*x(1)*x(3) + x(0)*x(2)*x(3)+ x(2);std::cout << "f:" << f << std::endl;// Constraints// SX g = vertcat(6 * x(0) + 3 * x(1) + 2 * x(2) - p(0), p(1) * x(0) + x(1) - x(2) - 1);SX g = vertcat(x(0)*x(1)*x(2)*x(3), pow(x(0),2) + pow(x(1),2) + pow(x(2),2) + pow(x(3),2));std::cout << "g:" << g << std::endl;// Initial guess and bounds for the optimization variablesvector<double> x0 = { 0.0, 0.0, 0.0, 0.0 };vector<double> lbx = { 1, 1, 1, 1 };vector<double> ubx = {5, 5, 5, 5 };// Nonlinear boundsvector<double> lbg = { 25, 40 };vector<double> ubg = { inf, 40 };// NLPSXDict nlp = { { "x", x }, { "f", f }, { "g", g } };// Create NLP solver and buffersFunction solver = nlpsol("solver", "ipopt", nlp);std::map<std::string, DM> arg, res;// Solve the NLParg["lbx"] = lbx;arg["ubx"] = ubx;arg["lbg"] = lbg;arg["ubg"] = ubg;arg["x0"] = x0;res = solver(arg);// Print the solutioncout << "--------------------------------" << endl;// std::cout << res << std::endl;cout << "objective: " << res.at("f") << endl;cout << "solution: " << res.at("x") << endl;return 0; }

結(jié)果：

djq@djq-UX410UQK:~/test/casadi_test/build$ ./casadi_test_node casadi_test x:[x_0, x_1, x_2, x_3] f:(((x_0*x_3)*((x_0+x_1)+x_2))+x_2) g:[(((x_0*x_1)*x_2)*x_3), (((sq(x_0)+sq(x_1))+sq(x_2))+sq(x_3))]****************************************************************************** This program contains Ipopt, a library for large-scale nonlinear optimization.Ipopt is released as open source code under the Eclipse Public License (EPL).For more information visit http://projects.coin-or.org/Ipopt ******************************************************************************This is Ipopt version 3.12.8, running with linear solver mumps. NOTE: Other linear solvers might be more efficient (see Ipopt documentation).Number of nonzeros in equality constraint Jacobian...: 4 Number of nonzeros in inequality constraint Jacobian.: 4 Number of nonzeros in Lagrangian Hessian.............: 10Total number of variables............................: 4variables with only lower bounds: 0variables with lower and upper bounds: 4variables with only upper bounds: 0 Total number of equality constraints.................: 1 Total number of inequality constraints...............: 1inequality constraints with only lower bounds: 1inequality constraints with lower and upper bounds: 0inequality constraints with only upper bounds: 0iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls0 4.1009029e+00 3.59e+01 1.54e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 01 6.3052937e+00 3.43e+01 2.33e+01 -1.0 5.89e+00 - 2.21e-03 4.20e-02h 12 5.3929003e+00 3.42e+01 7.45e+02 -1.0 3.89e+00 2.0 6.10e-06 3.54e-03F 13 6.6372159e+01 6.01e+00 2.27e+05 -1.0 3.78e+00 4.2 9.48e-04 4.80e-01h 24 9.6419121e+01 4.30e-01 5.82e+04 -1.0 7.23e+01 - 1.59e-02 1.00e+00h 15 9.4884972e+01 1.15e-03 3.12e+02 -1.0 1.47e+00 - 1.00e+00 1.00e+00h 16 8.7460064e+01 8.24e-02 1.95e+01 -1.0 6.98e-01 - 1.00e+00 1.00e+00f 17 8.9880566e+01 9.69e-03 3.14e+02 -1.0 7.37e-02 3.8 1.00e+00 1.00e+00h 18 8.9330308e+01 3.71e-04 1.71e+01 -1.0 2.19e-01 - 1.00e+00 1.00e+00f 19 8.9331900e+01 1.73e-06 4.10e+00 -1.0 2.16e-03 3.3 1.00e+00 1.00e+00h 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls10 8.0133699e+01 1.20e-01 1.86e+01 -1.0 2.30e+00 - 1.00e+00 1.00e+00f 111 8.2219265e+01 7.59e-03 3.27e+01 -1.0 6.41e-02 2.8 1.00e+00 1.00e+00h 112 7.5619844e+01 5.78e-02 1.78e+01 -1.0 2.89e+00 - 1.00e+00 1.00e+00f 113 7.6383207e+01 1.10e-03 4.23e+00 -1.0 2.53e-02 2.3 1.00e+00 1.00e+00h 114 5.6773756e+01 5.44e-01 1.90e+01 -1.0 1.15e+01 - 1.00e+00 1.00e+00f 115 6.0190720e+01 2.74e-02 5.29e+00 -1.0 1.24e-01 1.8 1.00e+00 1.00e+00h 116 2.8936531e+01 1.69e+00 2.27e+01 -1.0 3.26e+01 - 1.00e+00 1.00e+00f 117 3.1904315e+01 6.64e-02 1.11e+00 -1.0 1.93e-01 1.4 1.00e+00 1.00e+00h 118 2.0735088e+01 3.84e-01 1.76e+00 -1.0 9.22e+01 - 1.00e+00 1.99e-01f 119 1.7114152e+01 5.20e-01 8.02e+00 -1.0 4.71e+01 - 1.00e+00 1.30e-01f 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls20 1.7278457e+01 3.55e-02 1.54e-02 -1.0 4.07e-01 - 1.00e+00 1.00e+00h 121 1.7045230e+01 8.77e-03 6.88e-03 -1.7 4.41e-01 - 1.00e+00 1.00e+00h 122 1.7017006e+01 2.40e-03 2.52e-03 -2.5 3.47e-02 - 1.00e+00 1.00e+00h 123 1.7014119e+01 1.90e-04 1.03e-04 -3.8 6.30e-03 - 1.00e+00 1.00e+00h 124 1.7014020e+01 2.57e-07 3.19e-07 -5.7 3.46e-04 - 1.00e+00 1.00e+00h 125 1.7014017e+01 1.96e-11 2.80e-11 -8.6 3.31e-06 - 1.00e+00 1.00e+00h 1Number of Iterations....: 25(scaled) (unscaled) Objective...............: 1.7014017145174137e+01 1.7014017145174137e+01 Dual infeasibility......: 2.7976011905469220e-11 2.7976011905469220e-11 Constraint violation....: 1.9618084934336366e-11 1.9618084934336366e-11 Complementarity.........: 2.5297906848701540e-09 2.5297906848701540e-09 Overall NLP error.......: 2.5297906848701540e-09 2.5297906848701540e-09Number of objective function evaluations = 30 Number of objective gradient evaluations = 26 Number of equality constraint evaluations = 30 Number of inequality constraint evaluations = 30 Number of equality constraint Jacobian evaluations = 26 Number of inequality constraint Jacobian evaluations = 26 Number of Lagrangian Hessian evaluations = 25 Total CPU secs in IPOPT (w/o function evaluations) = 0.011 Total CPU secs in NLP function evaluations = 0.001EXIT: Optimal Solution Found.solver : t_proc (avg) t_wall (avg) n_evalnlp_f | 89.00us ( 2.97us) 87.07us ( 2.90us) 30nlp_g | 175.00us ( 5.83us) 163.31us ( 5.44us) 30nlp_grad_f | 110.00us ( 4.07us) 105.52us ( 3.91us) 27nlp_hess_l | 101.00us ( 4.04us) 95.68us ( 3.83us) 25nlp_jac_g | 84.00us ( 3.11us) 81.43us ( 3.02us) 27total | 21.84ms ( 21.84ms) 21.84ms ( 21.84ms) 1 -------------------------------- objective: 17.014 solution: [1, 4.743, 3.82115, 1.37941]

和用 CppAD 求解出來一樣：ipopt CppAD 非線性規(guī)劃

三. github：casadi_test

github：casadi_test

看到這里，點(diǎn)個贊吧！

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