some solvers for numerical optimization

This lib contains methods of line programming, feasible direction, quadratic programming, SQP and derivative-free algorithm. Using only C++ STL. This lib can solve medium or small scale problems, or be used for course experiments.

progress(this lib needs further implementation)

Derivative-free method is under development, and SQP and feasible direction methods do not support non-linear constraints cuurently. Moreover it's expected that more methods like unconstrained function solvers, and the documentation or help reference will be added in the future.

An SQP example

SQP method needs sub-libs of line programming and quadratic programming

#include <iostream>
#include "/include/mini_optim.h"
using namespace mini_optim;
using namespace std;
int main(int, char **)
{
    // define a obj_fun
    // see 'using obj_fun = std::function<double(std::vector<double> &)>;' in 'line_search.cpp'
    obj_fun f = [](vector<double> &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 standard input form for function sqp()
    sqp_i in;
    
    // primary point
    vector<double> x0 = {1, 0.5, 1, 0};
    
    // inequal constaints A*x>=b
    vector<vector<double>> A = {{-1, -1, -1, 0}, {-2, -3, -4, -5}};
    vector<double> b = {-3, -15};

    // equal constaints Aeq*x=beq
    // note: when equal constaints added, some primary points lead to the failure of the iteration. I'm figuring out what has caused the issue.
    // comment out the following 2 lines if it caused issue frequently
    vector<vector<double>> Aeq = {{1, 0, 2, 0}};
    vector<double> beq = {3};
    
    // assign the params
    in.Aeq = Aeq;
    in.beq = beq;
    in.A = A;
    in.b = b;
    in.x0 = x0;
    in.f = f;
    in.max_iter = 500;

    auto r1 = sqp(in);
    
    return 0;
}