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how to include a loop and stopping criteria in fmincon

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Rose WABUTI
Rose WABUTI on 24 Oct 2018
Edited: Torsten on 24 Oct 2018
I am using fmincon to slove a two stage optimization - the stackelberg leader follower type, by backward induction. The code below works but its too manual, the value of x calculated in the first stage is taken as the limit in the next stage and vise versa, I need to refine the code to include a stopping criteria such that when fval is non changing from the previous value and to not manually keeb changing the variable x as seen in the code I have changed the variable from b,c, z,d,. I need to include a loop but I don't know how, any idea?
fun =@(b)(-1)*( b(2)*( a - 2*(b(1) + b(2)) - (5 - b(2) + b(2)^2)) );
x0 = [0,1];
A = [];
B = [];
Aeq= [];
beq= [];
lb=[0,0];
ub=[1,1];
[b,fval(1)] = fmincon(fun,x0,[],[],Aeq,beq,lb,ub);
% leader observing followers responce choses the val
% fun =@(c)(-1)*( c(1)*( a - 2*(c(1) + c(2)) - (4 - c(1))) );
fun =@(c)(-1)*( c(1)*( a - 2*(c(1) + c(2)) - (4 - c(1) + c(1)^2)) );
lb=[0,b(2)];
ub=[1,b(2)];
[c,fval(2)] = fmincon(fun,x0,[],[],Aeq,beq,lb,ub);
%follower choses value in reaction to leaders
fun=@(z)(z(2)*( a - 2*(z(1) + z(2)) - (5 - z(2) + z(2)^2))*(-1));
x0 = [0,1];
A = [];
B = [];
Aeq= [];
beq= [];
lb=[c(1),0];
ub=[c(1),1];
[z,fval(3)] = fmincon(fun,x0,[],[],Aeq,beq,lb,ub);
%leader chooses value in reaction
% fun =@(d)(-1)*( d(1)*( a - 2*(d(1) + d(2)) - (4 - d(1))));
fun =@(d)(-1)*( d(1)*( a - 2*(d(1) + d(2)) - (4 - d(1) + d(1)^2)) );
lb=[0,z(2)];
ub=[1,z(2)];
[d,fval(4)] = fmincon(fun,x0,[],[],Aeq,beq,lb,ub);
% follower chooses value
fun=@(e)(e(2)*( a - 2*(e(1) + e(2)) - (5 - e(2) + e(2)^2))*(-1));
x0 = [0,1];
A = [];
B = [];
Aeq= [];
beq= [];
lb=[d(1),0];
ub=[d(1),1];
[e,fval(5)] = fmincon(fun,x0,[],[],Aeq,beq,lb,ub);

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