Fmincon Error: not enough input arguments

Hi,

I have to optimize parameters of a system of two ordinary differential equations. Therefore I wrote the following code. If I run the main file, I get the error: "not enough input arguments. Caused by: Failure in initial objective function evaluation. FMINCON cannot continue. " This error occurs in the obj1 function file, in the line, where the ode solver is used. If I uncomment the testparameters in the obj1 function, the error does not occur. Does anyone have an idea how to avoid this error?

p.s.: is this basically the right way to optimize the parameters of a system of ODEs or should it be done in a completely different way?

Main file:

        LB = zeros(1,8);
        x0  = LB;
        UB = [Inf,Inf,Inf,Inf,Inf,Inf,Inf,Inf];

 [x,fval] = fmincon(@obj1,x0,[],[],[],[],LB,UB);

Definition of function which I want to optimize

 function [flux] = obj1(K_a_F,K_a_T,K_b_F,K_b_T,r_a_F,r_a_T,r_b_F,r_b_T)

k1 = 10^-2; k_1 = 8* 10^-3; k2 = 10^-2; k_2 = 4*10^-3;

 %testparameters
 %K_a_F = 9.4*10^5; K_a_T = 3.9*10; K_b_F = 1.3*10^4; K_b_T = 1.2*10^-10;
 %r_a_F = 4.3*10^7; r_a_T = 4.2*10^9; r_b_F = 6.9*10^-7; r_b_T = 6.2*10^-9;

 a = 10^5;
 T0 = 27; T1 = 33;
 tscale = 1:3000;

 T = importdata('KursAT');
 F = importdata('kursAF');

 chiT = @(T) (-1/pi * (atan(a*(T-T1)) + atan(a*(T-T0))));

 Ft = @(x)interp1(tscale,F,x,'spline');
 Tt = @(x)interp1(tscale,T,x,'spline');

 [t,sol] = ode45(@(t,dyn) dynamics(t,dyn,Ft,Tt,K_a_F,K_a_T,K_b_F,K_b_T,r_a_F,r_a_T,r_b_F,r_b_T), [1,3000] , [60 30]);

 A = @(x)interp1(t,sol(:,1),x,'spline');
 B = @(x)interp1(t,sol(:,2),x,'spline');

 f = @(x,T,F,A,B) (chiT(T(x)).*(k2 *B(x)-k_2*T(x)) + chi_F(F(x),chiT,T(x)).*(k_1*A(x)-k1*F(x)));

 tau = 3000;
 flux = integral(@(x)f(x,Tt,Ft,A,B),0,tau);

Definition of ordinary differential equations

 function [ddyn] = dynamics(t,dyn,F,T,K_a_F,K_a_T,K_b_F,K_b_T,r_a_F,r_a_T,r_b_F,r_b_T)

 %kinetic parameters, unit: 1/s
 k1 = 10^-2; k_1 = 8* 10^-3; k2 = 10^-2; k_2 = 4*10^-3; 

 %Vmax for enzymes alpha and beta, unit: mM/s
 V_max_a = 1.6; V_max_b = 3.5;    

 %Michaelis-Menten constants for enzymes alpha and beta, unit: mM
 K_M_a = 1.5*10^-3; K_M_b = 2*10^-3;       

 ddyn = zeros(2,1);

 R_a_F = (K_a_F + r_a_F* F(t))./(K_a_F + r_a_F);
 R_a_T = (K_a_T + r_a_T* T(t))./(K_a_T + r_a_T);
 R_b_F = (K_b_F + r_b_F* F(t))./(K_b_F + r_b_F);
 R_b_T = (K_b_T + r_b_T* T(t))./(K_b_T + r_b_T);

 v_a = (V_max_a*dyn(1))./(K_M_a + dyn(1))*R_a_F *R_a_T;
 v_b = (V_max_b*dyn(2))./(K_M_b + dyn(2))*R_b_F *R_b_T;

 ddyn(1) = k1*F(t) + v_b - k_1*dyn(1) - v_a;
 ddyn(2) = k2*T(t) + v_a - k_2*dyn(2) - v_b;

Answer 1

[Matt J]

The objective obj1 that you've shown is a function of 8 separate scalar arguments. However, fmincon expects it to be a function of a single 1x8 vector argument. Re-write your input syntax for obj1 to give fmincon what it expects.

[Maximilian Ernst]

Hi, I have changed the code of obj1 to:

    function [flux] = obj1(x)

 k1 = 10^-2; k_1 = 8* 10^-3; k2 = 10^-2; k_2 = 4*10^-3; 
 %test
 %K_a_F = 9.4*10^5; K_a_T = 3.9*10; K_b_F = 1.3*10^4; K_b_T = 1.2*10^-10;
 %r_a_F = 4.3*10^7; r_a_T = 4.2*10^9; r_b_F = 6.9*10^-7; r_b_T = 6.2*10^-9;

 a = 10^5;
 T0 = 27; T1 = 33;
 tscale = 1:3000;

 T = importdata('KursAT');
 F = importdata('kursAF');

 chiT = @(T) (-1/pi * (atan(a*(T-T1)) + atan(a*(T-T0))));

 Ft = @(x)interp1(tscale,F,x,'spline');
 Tt = @(x)interp1(tscale,T,x,'spline');

 [t,sol] = ode45(@(t,dyn) dynamics(t,dyn,x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8)), [1,3000] , [60 30]);

 A = @(x)interp1(t,sol(:,1),x,'spline');
 B = @(x)interp1(t,sol(:,2),x,'spline');

 f = @(x,T,F,A,B) (chiT(T(x)).*(k2 *B(x)-k_2*T(x)) +        chi_F(F(x),chiT,T(x)).*(k_1*A(x)-k1*F(x)));

    tau = 3000;
    flux = integral(@(x)f(x,Tt,Ft,A,B),0,tau);

    end

but the same error still occurs. I am sorry but I have no idea why this could be.

[Matt J]

Forget about fmincon for a moment. What happens when you evaluate obj1 at the initial point, x0?

[Maximilian Ernst]

well, I get the same error

[Maximilian Ernst]

ah ok thank you! I accidently deleted the arguments Ft and Tt , in dynamics