Problem in fmincon solver

Question

Nikhil 2013-12-29

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/110948-problem-in-fmincon-solver

编辑： Walter Roberson 2014-1-4

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Hello all,

My aim is to solve for complicated non linear system of equations defined as follows:

Unknown variables: epsi, da, dr, phi1, Jr, Ja

Known variables: alpha= 40 deg, Z=16, Kn=4.5080*10(^5), Fr=Fa=17800

Equations are defined as follows:

epsi = 0.5 * (1 + da*tan(alpha) / dr)
phi1 = cosinv (-da*tan(alpha) / dr)
Jr=integration from -phi1 to phi1 of (1/(2*pi)) * (1 - (0.5/epsi) * (1-cos(theta) ) )^(1.5) * cos(theta)
Ja=integration from -phi1 to phi1 of (1/(2*pi)) * (1-(0.5/epsi) * (1-cos(theta) ) )^(1.5)
Fr / Fa = (Jr * cos(alpha)) / (Ja * sin(alpha))

To solve for these system of equations I am using fmincon function available in matlab..

My Matlab code is as follows:

    Z=16, KN1=4.5080e5; Fr=Fa=17800; alpha=40;
    %optimization for load distribution
    %KN1=Kn(5);
    %for i=1:1:length(Kn) 
     [dr, Epsi]=opt();
            function [dopt,EPSI] = opt()
            dr0=[0.08; 0.1];
            lb=[0, 0];
            ub=[1, 1];
            Options=optimset('Algorithm','active-set','Display','Iter');
            dopt=fmincon(@myfun,dr0,[],[],[],[],lb,ub,@mycon,Options);
            EPSI=myfun(dopt);
            end
                 function epsi=myfun(dr)
                 epsi=0.5*(1+dr(1)*tand(alpha)/(dr(2)));
                 end
                        function [c,ceq]=mycon(dr)
                        c=abs(-dr(1)*tand(alpha)/dr(2))-1;
                        phi1=acos(-dr(1)*tand(alpha)/dr(2));
                        epsi=0.5*(1+(dr(1)*tand(alpha)/dr(2)));
                        c=-1+(0.5/epsi).*(1-cos(phi1));
                        funr=@(theta)(1/(2*pi)).*(1-(0.5/epsi).*(1-cos(theta))).^(1.5).*cos(theta);
                        Jr=quad(funr,-phi1,phi1);
                        funa=@(beta)(1/(2*pi)).*(1-(0.5/epsi).*(1-cos(beta))).^(1.5);
                        Ja=quad(funa,-phi1,phi1);
                        ceq=real(Jr)*cosd(alpha)/(real(Ja)*sind(alpha))-Fr/Fa;
                        %c=[];
                        end

When I run this code, I am getting the optimized value of dr as [-0.0001, 0.0011]. This value is clearly beyond limiting values of dr. I am specifying lower bound of dr as [0,0]. I am unable to understand why Matlab is not considering specified boundaries. As well, my final answer is dependent on initial guess. If I change my initial guess then my final answer changes. Can somebody please help to resolve these issues??

Thanks in advance,

Nikhil

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Answer 1

Amit 2013-12-29

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/110948-problem-in-fmincon-solver#answer_119593

what's the exitflag?

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Nikhil 2014-1-4

Hey,

Sorry for getting back to you so late. Before using fmincon, I tried with fsolve. In this case the problem is in funr and funa terms. 1-(0.5/epsi)*(1-cos(theta or beta)) term can become negative. In this case then -ve term raise to odd power can give imaginary results. Hence I need to impose constraints at each iteration, to check whether above mentioned term is positive.

Nikhil 2014-1-4

more over when I analyzed my error, I am getting following information:

fmincon stopped because the predicted change in the objective function is less than the default value of the function tolerance but constraints are not satisfied to within the default value of the constraint tolerance.

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