Question regarding passing input arguments in fmincon

Question

Deepa Maheshvare 2019-4-23

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/457960-question-regarding-passing-input-arguments-in-fmincon

编辑： Deepa Maheshvare 2019-4-26

Hi All,

I am solving an optimization problem.There are no equality constraints in my model. I want to pass ODEs as constraint to fmincon using,non-linear constraint, nlcon argument .

The function model contains odes

function dz = model(t, z, c)  
              dz(1) = ..
              dz(2) = ..

I'd like to ask how the ode intergrator has to be called in the place of nlcon in fmincon(@objective,p0,A,b,Aeq,beq,lb,ub,nlcon).

%p0 = Initial Value of Parameters
A = [];
b = [];
Aeq = [];
beq = [];
nlcon  = ode45(@(t,z)model(t,z,x), tSpan, z0); % Is this correct?
p = fmincon(@objective,p0,A,b,Aeq,beq,lb,ub,nlcon); 

Since the ode function is already called in nlcon , is it required to call the function model again inside the objective function?

function cost = objective(c,time_exp,expZ,tSpan,z0)
sol = ode45(@(t,z)model(t,z,c), tSpan, z0); % Is this step required?
ModelZ = deval(sol, time_exp);
cost = ModelZ-expZ;

Any help would be highly appreciated.

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Deepa Maheshvare 2019-4-23

编辑：Deepa Maheshvare 2019-4-23

在 MATLAB Online 中打开

Thanks a lot for the response. I went through the details posted in the above-mentioned link.

Since the time series data was avilable in the example shown in the link, lsqcurvefit has been used.

In my case, I don't have the time series experimental data.

My real system is quite large, 100 odes , I am trying to perform global optimization.The data that I have from the experiments is steady state values of the variables z1,z2 and so on.

Probably my objective function should be modified as,

function cost = objective(c,expZ,tSpan,z0)
sol = ode45(@(t,z)model(t,z,c), tSpan, z0); % Is this step required?
ModelZ = sol(end,:)%  the solutions obtained from model at end point of tSpan
cost = ModelZ-expZ; %expZ contains steady state values of z1,z2.. 

since time_exp is the steady state time(not a vector).

Please note: I have upper and lower bounds (lb,ub)defined on the parameters that have to be estimated.

Could you please suggest how to proceed ?

Deepa Maheshvare 2019-4-24

编辑：Deepa Maheshvare 2019-4-24

在 MATLAB Online 中打开

Thank you very much. Yes, I want to do this "restrict the values of the solution at all times to be in a certain range, not just the final values".

May I ask a doubt regarding the implementation of this,"In "nlcon", choose an n-dimensional vector of time instants "tspan", solve the ODEs at these time instants "

tSpan = [0 2000] % in s 
nonlincon  = ode45(@(t,z)model(t,z,x), tSpan, z0);
% ode45(@(t,z)model(t,z,x), tSpan, z0); will return a matrix of dimension that is equal to(no. of time steps*m) m= the length of the vector z i.e. the number of variables z1,z2..,zm
x = fmincon(objective,x0,A,b,Aeq,beq,lb,ub,nonlincon);

From what you have explained, ncoln should be a vector (or matrix?)of dimension m*n i.e. 2*n (m = 2 , when z = z1,z2), where m is the number of variables and n is the number of timesteps. (Or 2 referes to upper bound and lower bound?).Please correct me if my understanding is wrong.

Could you please explain a bit more on this? 2*n - dimensional constraint vector c with lb(i) <= c(2*i-1), ub(i) >= c(2*i) (i=1,...,n).

The vector c, in my example in my original post, contains the initial values of the parametres that I want to estimate. I think here you are referring 'c' to the dimension of the vector returned

in nonlincon.

Also, in my original post, lb and ub is specified for the parameters in fmincon, for the paramters.

"lb(i) <= c(2*i-1), ub(i) >= c(2*i) (i=1,...,n)." Are these(lb, ub) for the variables(i.e z1,z2)?

Deepa Maheshvare 2019-4-26

编辑：Deepa Maheshvare 2019-4-26

在 MATLAB Online 中打开

Hi Torsten,

Thanks a ton for all the clarifications.

Since my model is in xml file , I am using SimBiology toolbox .I have created a model object using

modelObj = sbmlimport('Model.xml')

cs = getconfigset(modelObj);

cs.SolverType = 'ode15s';

cs.StopTime = 24;

[t, x, names] = sbiosimulate(modelObj);

There is a function call available for parameter estimation in SimBiology toolbox.

sbiofit(model,estimatedParam,'fmincon')

However, I am not sure how the input arguments of the estimation method,fmincon, has to be passed.I have a confusion here,

I've already specified p0,lb,ub in estimatedParam array with properties Name, InitialValue and Bounds

estimatedParams     = estimatedInfo(paramsToEstimate,'InitialValue',ParameterInitialValues,'Bounds',ParameterBounds)

Moreover, for the other arguments that have to be passed in the function call to fmincon,

fmincon(@objective,p0,A,b,Aeq,beq,lb,ub,nlcon)

p0 , lb,ub are already defined in estimatedParam in sbiofit(model,estimatedParam,'fmincon')

I'm not sure how to set up A=[],b=[],Aeq=[],beq = [] and define nlcon since the model is in xml format.

Could you please provide some suggestions on how to proceed?

Torsten 2019-4-26

Sorry, but I don't have experience with the SimBiology toolbox.

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Answer 1

Alan Weiss 2019-4-23

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/457960-question-regarding-passing-input-arguments-in-fmincon#answer_371836

I am not sure that I understand what you mean by "I want to pass ODEs as a constraint to fmincon." What about the ODE solution is a constraint? Do you want the minimum value of the solution to be above zero? Do you want the ODE solution to lie in a certain box? Once you explicitly define what you mean by the ODE solution is a "constraint," then I think that the answer to your question will be obvious. You will solve the ODE, get sol, and then write the constraint in terms of sol, maybe fun(deval(sol,tspan)) for some appropriate function fun and set of times tspan.

Alan Weiss

MATLAB mathematical toolbox documentation

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Deepa Maheshvare 2019-4-23

Hi,

I'm sorry , I haven't explained it clearly.

"Maybe you are trying to fit your ODE solution to some observed (measured) values as a function of time."

No, the experimental measurements are all steady state values. For example , for the variable z1, there are 5 experimental studies that report the steady state value from experiment(z1_exp1,z1_exp2,z1_exp3,z1_exp4,z1_exp5). This gives me a range i.e. bound

z1_max and z1_min.

With z1_max and z1_min as the constraint , I wish to do the following

" restrict the values of the solution at all times to be in a certain range, not just the final values".Therefore, I am not sure whether it is appropriate to use lsqcurvefit ,used in the suggestions provided,for my problem.

Alan Weiss 2019-4-23

Sorry, I am unable to understand what you are trying to do, so this will be my last reply. I suggest that you write out equations or inequalities describing your constraint. Seriously, write them down. Then, given those equations or inequalities, you can write a corresponding nonlinear constraint function in fmincon syntax, restricting the result by using deval on the solution at relevant times. If you don't understand what I am suggesting, sorry, maybe someone else can help.

Alan Weiss

MATLAB mathematical toolbox documentation

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