Error using fmincon, the function cannot continue

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Andrea Mazzetto
Andrea Mazzetto on 15 Jun 2021
Commented: Andrea Mazzetto on 21 Jun 2021
Hi, everyone.
I'm trying to optimize a function with 8 optimization variables. I set up initial point and costraints but appears the following error:
"Error using optim.problemdef.OptimizationProblem/solve
Objective function is undefined at initial point. Fmincon cannot continue.
Error in curvatura_V7 (line 75)
[sol,fval,exitflag,output] = solve(prob,x0);"
the code is as follow:
aymax = 5;
V = 70;
deltay = 60;
deltax = 3;
intorno = sqrt(deltax^2+deltay^2);
dmin = 3;
type objfun
rof1 = optimvar('rof1');
rof2 = optimvar('rof2');
rof3 = optimvar('rof3');
rof4 = optimvar('rof4');
sf1 = optimvar('sf1');
sf2 = optimvar('sf2');
sf3 = optimvar('sf3');
sf4 = optimvar('sf4');
obj = fcn2optimexpr(@objfun,rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4);
prob = optimproblem('Objective',obj);
constr1 = (-aymax / (V/3.6)^2) <= rof1;
prob.Constraints.curvatura1 = constr1;
constr2 = (aymax / (V/3.6)^2) >= rof1;
prob.Constraints.curvatura1 = constr2;
constr3 = (-aymax / (V/3.6)^2) <= rof2;
prob.Constraints.curvatura2 = constr3;
constr4 = (aymax / (V/3.6)^2) >= rof2;
prob.Constraints.curvatura2 = constr4;
constr5 = (-aymax / (V/3.6)^2) <= rof3;
prob.Constraints.curvatura3 = constr5;
constr6 = (aymax / (V/3.6)^2) >= rof3;
prob.Constraints.curvatura3 = constr6;
constr7 = (-aymax / (V/3.6)^2) <= rof4;
prob.Constraints.curvatura4 = constr7;
constr8 = (aymax / (V/3.6)^2) >= rof4;
prob.Constraints.curvatura4 = constr8;
constr9 = sf1 >= 0 ;
prob.Constraints.ascissa1 = constr9;
constr10 = sf1 <= sf2;
prob.Constraints.ascissa1 = constr10;
constr11 = sf2 >= sf1;
prob.Constraints.ascissa2 = constr11;
constr12 = sf2 <= sf3;
prob.Constraints.ascissa2 = constr12;
constr13 = sf3 >= sf1+sf2;
prob.Constraints.ascissa3 = constr13;
constr14 = sf3 <= sf4;
prob.Constraints.ascissa3 = constr14;
constr15 = sf4 >= sf1+sf2+sf3;
prob.Constraints.ascissa4 = constr15;
constr16 = sf4 <= 2*intorno;
prob.Constraints.ascissa4 = constr16;
show(prob)
x0.rof1 = 0;
x0.rof2 = 0;
x0.rof3 = 0;
x0.rof4 = 0;
x0.sf1 = 0;
x0.sf2 = 0;
x0.sf3 = 0;
x0.sf4 = 0;
[sol,fval,exitflag,output] = solve(prob,x0);

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Accepted Answer

Walter Roberson
Walter Roberson on 19 Jun 2021
Ran in:
aymax = 5;
V = 70;
deltay = 60;
deltax = 3;
intorno = sqrt(deltax^2+deltay^2);
dmin = 3;
rof1 = optimvar('rof1');
rof2 = optimvar('rof2');
rof3 = optimvar('rof3');
rof4 = optimvar('rof4');
sf1 = optimvar('sf1');
sf2 = optimvar('sf2');
sf3 = optimvar('sf3');
sf4 = optimvar('sf4');
obj = fcn2optimexpr(@objfun,rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4);
Warning: Inf or NaN value encountered.
Warning: Inf or NaN value encountered.
Warning: Inf or NaN value encountered.
Warning: Inf or NaN value encountered.
Warning: Inf or NaN value encountered.
Warning: Inf or NaN value encountered.
prob = optimproblem('Objective',obj);
constr1 = (-aymax / (V/3.6)^2) <= rof1;
prob.Constraints.curvatura1 = constr1;
constr2 = (aymax / (V/3.6)^2) >= rof1;
prob.Constraints.curvatura1 = constr2;
constr3 = (-aymax / (V/3.6)^2) <= rof2;
prob.Constraints.curvatura2 = constr3;
constr4 = (aymax / (V/3.6)^2) >= rof2;
prob.Constraints.curvatura2 = constr4;
constr5 = (-aymax / (V/3.6)^2) <= rof3;
prob.Constraints.curvatura3 = constr5;
constr6 = (aymax / (V/3.6)^2) >= rof3;
prob.Constraints.curvatura3 = constr6;
constr7 = (-aymax / (V/3.6)^2) <= rof4;
prob.Constraints.curvatura4 = constr7;
constr8 = (aymax / (V/3.6)^2) >= rof4;
prob.Constraints.curvatura4 = constr8;
constr9 = sf1 >= 0 ;
prob.Constraints.ascissa1 = constr9;
constr10 = sf1 <= sf2;
prob.Constraints.ascissa1 = constr10;
constr11 = sf2 >= sf1;
prob.Constraints.ascissa2 = constr11;
constr12 = sf2 <= sf3;
prob.Constraints.ascissa2 = constr12;
constr13 = sf3 >= sf1+sf2;
prob.Constraints.ascissa3 = constr13;
constr14 = sf3 <= sf4;
prob.Constraints.ascissa3 = constr14;
constr15 = sf4 >= sf1+sf2+sf3;
prob.Constraints.ascissa4 = constr15;
constr16 = sf4 <= 2*intorno;
prob.Constraints.ascissa4 = constr16;
show(prob)
OptimizationProblem : Solve for: rof1, rof2, rof3, rof4, sf1, sf2, sf3, sf4 minimize : objfun(rof1, rof2, rof3, rof4, sf1, sf2, sf3, sf4) subject to curvatura1: 0.013224 >= rof1 subject to curvatura2: 0.013224 >= rof2 subject to curvatura3: 0.013224 >= rof3 subject to curvatura4: 0.013224 >= rof4 subject to ascissa1: sf1 - sf2 <= 0 subject to ascissa2: sf2 - sf3 <= 0 subject to ascissa3: sf3 - sf4 <= 0 subject to ascissa4: sf4 <= 120.1499
x0.rof1 = 0;
x0.rof2 = 0;
x0.rof3 = 0;
x0.rof4 = 0;
x0.sf1 = 0;
x0.sf2 = 0;
x0.sf3 = 0;
x0.sf4 = 0;
%[sol,fval,exitflag,output] = solve(prob,x0);
result = objfun(x0.rof1, x0.rof2, x0.rof3, x0.rof4, x0.sf1, x0.sf2, x0.sf3, x0.sf4)
Warning: Inf or NaN value encountered.
Warning: Inf or NaN value encountered.
Warning: Inf or NaN value encountered.
Warning: Inf or NaN value encountered.
Warning: Inf or NaN value encountered.
Warning: Inf or NaN value encountered.
Warning: Inf or NaN value encountered.
Warning: Inf or NaN value encountered.
result = NaN
function erroredistanza = objfun(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4)
deltay = 60;
deltax = 3;
tau0 = 90;
tau0 = deg2rad(tau0);
dmin = 3;
roi1=0;
si1=0;
PSI1 = @(roi1,rof1,si1,sf1,s) tau0 + ((rof1*si1-roi1*sf1)/(si1-sf1))*s + ((roi1-rof1)/(si1-sf1))*(s.^2)/2;
PSI2 = @(rof1,rof2,sf1,sf2,s) ((rof2*sf1-rof1*sf2)/(sf1-sf2))*s + ((rof1-rof2)/(sf1-sf2))*(s.^2)/2;
PSI3 = @(rof2,rof3,sf2,sf3,s) ((rof3*sf2-rof2*sf3)/(sf2-sf3))*s + ((rof2-rof3)/(sf2-sf3))*(s.^2)/2;
PSI4 = @(rof3,rof4,sf3,sf4,s) ((rof4*sf3-rof3*sf4)/(sf3-sf4))*s + ((rof3-rof4)/(sf3-sf4))*(s.^2)/2;
funx1 = @(roi1,rof1,si1,sf1,s) integral(@(s) cos(PSI1(roi1,rof1,si1,sf1,s)),0,sf1);
funx2 = @(rof1,rof2,sf1,sf2,s) integral(@(s) cos(PSI2(rof1,rof2,sf1,sf2,s)),sf1,sf2);
funx3 = @(rof2,rof3,sf2,sf3,s) integral(@(s) cos(PSI3(rof2,rof3,sf2,sf3,s)),sf2,sf3);
funx4 = @(rof3,rof4,sf3,sf4,s) integral(@(s) cos(PSI4(rof3,rof4,sf3,sf4,s)),sf3,sf4);
funy1 = @(roi1,rof1,si1,sf1,s) integral(@(s) sin(PSI1(roi1,rof1,si1,sf1,s)),0,sf1);
funy2 = @(rof1,rof2,sf1,sf2,s) integral(@(s) sin(PSI2(rof1,rof2,sf1,sf2,s)),sf1,sf2);
funy3 = @(rof2,rof3,sf2,sf3,s) integral(@(s) sin(PSI3(rof2,rof3,sf2,sf3,s)),sf2,sf3);
funy4 = @(rof3,rof4,sf3,sf4,s) integral(@(s) sin(PSI4(rof3,rof4,sf3,sf4,s)),sf3,sf4);
funx = @(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) funx1(roi1,rof1,si1,sf1) + funx2(rof1,rof2,sf1,sf2) + funx3(rof2,rof3,sf2,sf3) + funx4(rof3,rof4,sf3,sf4);
funy = @(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) funy1(roi1,rof1,si1,sf1) + funy2(rof1,rof2,sf1,sf2) + funy3(rof2,rof3,sf2,sf3) + funy4(rof3,rof4,sf3,sf4);
fun2x =@(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) funx(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) - deltax;
fun2y =@(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) funy(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) - deltay;
fun3x =@(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) fun2x(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4).^2;
fun3y =@(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) fun2y(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4).^2;
d =@(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) sqrt(fun3x(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) + fun3y(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4));
erroredistanza = d(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) - dmin;
end
... Look at the code. You divide by (si1-sf1) and (sf1-sf2) and (sf2-sf3) and (sf3-sf4) . si1 is 0, and sf1 to sf4 are passed in. Your initial values for all of the variables is 0, so you are dividing by (0-0) in multiple places.
If you divide by something in your objective, it is your responsibility to ensure that your constraints exclude the possibility that you are going to be dividing by 0, and that your initial point is not going to trigger a division by 0.

More Answers (1)

Tarunbir Gambhir
Tarunbir Gambhir on 18 Jun 2021
The error message says the objective function is not defined at initial point. This means objfun(xo) returns a 'NaN' or errors out (where "objfun" is objective function and "xo" is the initial point). It could be that the initial point does not satisfy all the provided constraints for the objective function. Since you did not provide the 'objfun', I would not be able to help any further.
Anyway, to avoid this error you can simply try choosing a better initial point.
  1 Comment
Andrea Mazzetto
Andrea Mazzetto on 19 Jun 2021
this is my objfun
function erroredistanza = objfun(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4)
deltay = 60;
deltax = 3;
tau0 = 90;
tau0 = deg2rad(tau0);
dmin = 3;
roi1=0;
si1=0;
PSI1 = @(roi1,rof1,si1,sf1,s) tau0 + ((rof1*si1-roi1*sf1)/(si1-sf1))*s + ((roi1-rof1)/(si1-sf1))*(s.^2)/2;
PSI2 = @(rof1,rof2,sf1,sf2,s) ((rof2*sf1-rof1*sf2)/(sf1-sf2))*s + ((rof1-rof2)/(sf1-sf2))*(s.^2)/2;
PSI3 = @(rof2,rof3,sf2,sf3,s) ((rof3*sf2-rof2*sf3)/(sf2-sf3))*s + ((rof2-rof3)/(sf2-sf3))*(s.^2)/2;
PSI4 = @(rof3,rof4,sf3,sf4,s) ((rof4*sf3-rof3*sf4)/(sf3-sf4))*s + ((rof3-rof4)/(sf3-sf4))*(s.^2)/2;
funx1 = @(roi1,rof1,si1,sf1,s) integral(@(s) cos(PSI1(roi1,rof1,si1,sf1,s)),0,sf1);
funx2 = @(rof1,rof2,sf1,sf2,s) integral(@(s) cos(PSI2(rof1,rof2,sf1,sf2,s)),sf1,sf2);
funx3 = @(rof2,rof3,sf2,sf3,s) integral(@(s) cos(PSI3(rof2,rof3,sf2,sf3,s)),sf2,sf3);
funx4 = @(rof3,rof4,sf3,sf4,s) integral(@(s) cos(PSI4(rof3,rof4,sf3,sf4,s)),sf3,sf4);
funy1 = @(roi1,rof1,si1,sf1,s) integral(@(s) sin(PSI1(roi1,rof1,si1,sf1,s)),0,sf1);
funy2 = @(rof1,rof2,sf1,sf2,s) integral(@(s) sin(PSI2(rof1,rof2,sf1,sf2,s)),sf1,sf2);
funy3 = @(rof2,rof3,sf2,sf3,s) integral(@(s) sin(PSI3(rof2,rof3,sf2,sf3,s)),sf2,sf3);
funy4 = @(rof3,rof4,sf3,sf4,s) integral(@(s) sin(PSI4(rof3,rof4,sf3,sf4,s)),sf3,sf4);
funx = @(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) funx1(roi1,rof1,si1,sf1) + funx2(rof1,rof2,sf1,sf2) + funx3(rof2,rof3,sf2,sf3) + funx4(rof3,rof4,sf3,sf4);
funy = @(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) funy1(roi1,rof1,si1,sf1) + funy2(rof1,rof2,sf1,sf2) + funy3(rof2,rof3,sf2,sf3) + funy4(rof3,rof4,sf3,sf4);
fun2x =@(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) funx(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) - deltax;
fun2y =@(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) funy(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) - deltay;
fun3x =@(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) fun2x(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4).^2;
fun3y =@(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) fun2y(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4).^2;
d =@(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) sqrt(fun3x(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) + fun3y(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4));
erroredistanza = d(rof1,rof2,rof3,rof4,sf1,sf2,sf3,sf4) - dmin;

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