$\begingroup$Minimize the following objective function over $(x_1,x_2)$
$$f (x_1, x_2) := \exp(x_1) \, (4 x_1^2 + 2 x_2^2 + 4 x_1 x_2 + 2 x_2 + 1) + b$$
subject to the constraints
$$x_1^2 + x_2 = 1 - b \qquad \qquad -x_1 x_2 \leq 10$$
Note that $b$ is also in one of the constraints.
I want to run the optimization 20 times, for b=1, b=2, b=3.....b=20 ( because b is between 0 to 20). I also want to store the optimal (x(1),x(2),b) so that I can plot it later.
There are existing reference (()) which I followed. How do I modify the following code so that it will do the above?
Step 1: Write a file objfun.m.
function f = objfun(x) f = exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1)+b; Step 2: Write a file confuneq.m for the nonlinear constraints.
function [c, ceq] = confuneq(x) % Nonlinear inequality constraints c = -x(1)*x(2) - 10; % Nonlinear equality constraints ceq = x(1)^2 + x(2) - 1+b; Step 3: Invoke constrained optimization routine.
x0 = [-1,1]; % Make a starting guess at the solution options = optimoptions(@fmincon,'Algorithm','sqp'); [x,fval] = fmincon(@objfun,x0,[],[],[],[],[],[],... @confuneq,options); Update:
I tried to modified my objective function by adding the b,
function f = objfun(x,b) f = exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1)+b; and I got
Error using objfun (line 2) Not enough input arguments.Error in fmincon (line 640) initVals.f = feval(funfcn{3},X,varargin{:}); Caused by: Failure in initial user-supplied objective function evaluation. FMINCON cannot continue. 1 Answer
$\begingroup$I haven't tested this, but something like it should work.
First, modify objfun so that b is an input arg. Then try this:
cnt = 1; xopt = []; fval = []; for b = 1 : 20 cfun = @(x)objfun(x,b); [xopt(cnt),fval(cnt)] = fmincon(cfun,[-1 1],[],[],[],[],[],[],... @confuneq,options); cnt = cnt + 1; end 
