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    %% Linear Inequality and Equality Constraint  
% Find the minimum value of Rosenbrock's function when there are both a
% linear inequality constraint and a linear equality constraint.   

% Copyright 2015 The MathWorks, Inc.


%% 
% Set the objective function |fun| to be Rosenbrock's function. 
fun = @(x)100*(x(2)-x(1)^2)^2 + (1-x(1))^2;  

%% 
% Find the minimum value starting from the point |[0.5,0]|, constrained
% to have $x(1) + 2x(2) \le 1$ and $2x(1) + x(2) = 1$. 
%  
% * Express the linear inequality constraint in the form |A*x <= b| by taking
% |A = [1,2]| and |b = 1|.  
% * Express the linear equality constraint in the form |Aeq*x <= beq| by
% taking |Aeq = [2,1]| and |beq = 1|.   
x0 = [0.5,0];
A = [1,2];
b = 1;
Aeq = [2,1];
beq = 1;
x = fmincon(fun,x0,A,b,Aeq,beq)