系统优化与调度——非线性规划问题：梯度投影法之MATLAB实现

System Optimization and Scheduling 

Midterm Project 

1.       Give a non-quadratic nonlinear objective function and linear inequality constraints (at least two).

2.       Select a computational method (primal or dual) for constrained optimization you learn in the class.

3.       Show your computational results and corresponding analysis. 

4.       Submit the typed report.

5.       Attach your program. 

这是之前选的一门研究生的课的期中作业。用梯度投影法解决了非线性规划问题。开始找了一份百度文库的代码，但那个代码有问题要改好多。现在至少自己试的几个test case和MATLAB自带的函数计算结果相同。

main.m

syms x1 x2 x3;
% f=2*x1^2+2*x2^2-2*x1*x2^3-4*x1^7-6*x2;
% var=[x1,x2];
% valst=[-1,-1];
% A=[1 1;1 5;-1 0;0 -1];
% b=[2 5 0 0]';
% f=x1^3+x2^2-2*x1-4*x2+6;
% var=[x1,x2];
% valst=[0 0];
% A=[2,-1;1,1;-1,0;0,-1];
% b=[1 2 0 0]';
var=[x1,x2,x3];
valst=[10,10,10];
f=-x1*x2*x3;
A=[-1,-2,-2;1,2,2];
b=[0 72]';
[x,mimfval]=MinRosenGradientProjectionMethod(f,A,b,valst,var)
[x2,fval]=fmincon('confun',valst,A,b)

MinRosenGradientProjectionMethod.m

function [x,minf]=MinRosenGradientProjectionMethod(f,A,b,x0,var,eps)
%f is the objection function;
%