Optimization with several objectives

Hi everybody, I hope you can help me with the following issue. Let us assume I've a couple of data sets and I want to fit these data to a dynamical non-linear first order models. Each model has two charateristic parameters but they also share a couple of parameters. That is, there is a k1 and k2 for the first model and k3/k4 for the second model but they have k and a that are in both models. Which Matlab tool/algorithm should I use?. In this case k1 and k2 are computed to minimise the squared residual error among the first data set and the first model(as k3 and k4 with the second model) but k and alpha should be computed to minimise the squared residual error among the data sets and the models...

Thank you very much in advance.

Answer 1

[Matt J]

You might want to elaborate on your terminology "dynamical non-linear first order model". Do you have a closed form expression (in parameters k1,...k4,k,alpha) for the function you are trying to fit, or are there differential equations involved?

If you are fitting multiple explicit scalar-valued functions, just view them simultaneously as a single, vector valued function with parameters k1,..,k4,k,alpha. You can fit functions, vector-valued or scalar-valued, with lsqcurvefit, for example.

[EFREN]

Hi Matt, thanks for your time and answer. Let me explain a little bit more about the issue. I have a couple dynamical models: dV1/dt=f1(k1,k2,k,a) ; dV2/dt=f2(k3,k3,k,a) and I also have experimental measurements: V1* and V2*. I would like to estimate parameters k1,...k4,k,a. First, I thought that k1 and k2 could be estimated minimizing (V1-V1*)*(V1-V1*) (as k3 and k4 with V2 and V2* whereas the common parameters: k and a should be estimated with(V1-V1*)*(V1-V1*)+(V2-V2*)*(V2-V2*). My question now is what is better: to maintain your proposal (i.e. estimate all the parameters with min (V1-V1*)*(V1-V1*)+(V2-V2*)*(V2-V2*)? or to carry out the estimation according to my proposal? Which are the advantages/disadvantages of these proposals. Thanks again in advance

[Matt J]

Joint estimation based on (V1-V1*)*(V1-V1*)+(V2-V2*)*(V2-V2*) can be expected to give more accurate estimates because all parameters are then estimated based on more data.

However, the other scheme might be a good way to generate an initializer for the joint estimation, if it is computationally simple.