function fmincon() with C++

This repository is based on C++ numerical lib armadillo, and implements one of the frequently used functions fmincon(). It can be a choosable alternative for part of optimization needs.

algorithms

1. BFGS (default when the constraint is empty)
2. Powell
3. modified Powell in Sargent form (default when BFGS fails)
4. Rosenbrock
5. mutiplier (it will be used with one of the methods above when there are constraints)

6. exterior-point (legacy)

   Examples:

   when the gradient is not given or unsolvable

   #include <iostream>
   #include <cmath>
   #include "sci_arma.h"
   int main() {
   //define a obj_fun
   obj_fun f = [](vec& x)-> double {
       return pow(1 - 0.1 * x(0), 2) + 100 * pow(x(1) - 0.5 * x(0) * x(0), 2)
           + pow(1 - 0.1 * x(2), 2) + 100 * pow(x(3) - 0.5 * x(2) * x(2), 2);
   };
   
   //define a start point
   vec x0 = { 1,1,1,1 };
   
   //optimization without constraints
   //using default algorithm BFGS
   auto result1 = sci_arma::fmincon(f, x0);
   
   //define linear constraints Ax<=b
   mat A = { {1,1,1,0},{2,3,4,5} };
   vec b = { 3,15 };
   
   //optimization with inequality linear constraints
   auto result2 = sci_arma::fmincon(f, x0, A, b);
   
   //define linear equality constraints
   mat Aeq = { {1,0,2,0} };
   vec beq = { 3 };
   
   //optimization with mixed linear constraints
   auto result3 = sci_arma::fmincon(f, x0, A, b, Aeq, beq);
   
   //define non-linear inequality constraints c(x)<=0
   auto c = [](vec& x)->vec {
       vec temp = { 25 * x(0) * x(0) + x(1) * x(1) + x(2) * x(2) + x(3) * x(3) - 50 * x(3) };
       return temp;
   };
   
   //optimization with mixed constraints
   //set options::algorithm from preset(Powell_modified) to Powell
   options opt;
   opt.algo = Powell;
   auto result4 = sci_arma::fmincon(f, x0, A, b, Aeq, beq, c, opt);
   
   //output
   std::cout << result1;
   std::cout << endl;
   std::cout << result2;
   std::cout << endl;
   std::cout << result3;
   std::cout << endl;
   std::cout << result4;
   return 0;
   }

   or when the gradient is given

   #include <iostream>
   #include <cmath>
   #include "sci_arma.h"
   int main() {
   //define a obj_fun
   obj_fun f = [](vec& x)-> double {
       return pow(1 - 0.1 * x(0), 2) + 100 * pow(x(1) - 0.5 * x(0) * x(0), 2)
           + pow(1 - 0.1 * x(2), 2) + 100 * pow(x(3) - 0.5 * x(2) * x(2), 2);
   };
   
   //define the gradient
   gradient g = [](vec& x)->vec {
       vec result = { -0.2 * (1 - 0.1 * x(0)) - 200 * x(0) * (x(1) - 0.5 * x(0) * x(0)),
                    200 * (x(1) - 0.5 * x(0) * x(0)),
                    -0.2 * (1 - 0.1 * x(2)) - 200 * x(2) * (x(3) - 0.5 * x(2) * x(2)),
                    200 * (x(3) - 0.5 * x(2) * x(2)) };
       return result;
   };
   
   options opt;
   opt.gra = g;
   opt.enable_self_defined_gra = true;
   opt.max_ite = 5000;
   vec x0 = { 0,0,0,0 };
   auto result1 = sci_arma::fmincon(f, x0, opt);
   std::cout << result1 << endl;
   return 0;
   }