Thanks Aly.

The nonlinear constraints are due to a product of binary variables and real variables. How to linearize such constraints in Matlab?

Example:

min O.F

s.t

y+x.H=0

y,x>=0 

H is binary var

You can solve the problem two times, one time with H=0, and second time with H=1, if H is a single valued binary variable. Linearization for this problem doesn't mean.

Dear Prof Seyed,

Thank you for your answer. I will do that, but after solving the model once with H=1, and once by H=0, what should I do with the decision variables and the objective function? Should I take the mean of these values or what?

Thank you in advance.

I  just read this message roughly and come to my mind the idea : if you want to linearize nonlinear problem, one may use Taylor series. It means that the nonlinear function is linearized using Taylor series up to certain order (as Euler formula has been developed,etc). You can take a special point to start the linearization, for instance the point where the nonlinear function reach equilibrium (zero value of df/dx). 

Dear Dr Hanna,

Thank you for your reply,

I think Taylor series works with continuous functions. However, my model is mixed integer nonlinear programming, and the nonlinear term is a set of constraints.

The solver or platform you use is not the problem. The problem is the linearization structure you need to use.

In this case, if H is a binary variable and X is a continous variable you may declare another variable Y, for example and declare constraints based on an upper bound of X. In this way:

Let be M an upper bound of X, H a binary variable and Y a continous substitute variable:

1. Upper bound of the substitute variable Y:

Y = 0

Use this 4 constraints and you will have a linearized mathematical formulation.

Dear Prof Isaza,

Thank you for your interesting answer.

My modest experience with this tricky method is unstable in computations.

 Yes, the "tricky" part part is to calculate or estimate an upper bound of the continous variable. Once you do that, the method works fine.

In the manual, it is easy to find linearlization option.

I am very surprised many researcher did not know the simple and important information of LINDO products.

1. Demo version, manuals and Linus textbooks are free. If English speakers read those book, you can understand the Set expression and others. If you can understand Japanese, see my announcement of DEA, Cancer Gene Diagnosis, several translations and original two books.

2. Linus reviewed many papers and books. He made over 500 sample models. I need not survey the papers and develop new approach about DEA model by modification of sample DEA.

3. Linus explains many sample models. Data are defined in Data section. But, you define those data on Excel. You can read it by @OLE function and output Excel. If you must a big data, you choose the DB.

4. I developed “100-fold cross validation for small sample method and Matryoshka Feature Selection method for microarray datasets.” See the Chap.2 and Chap.9 of my Springer book (2016).

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My

answer is not proper.

LINDO Systems inc. developes the linearlization option for many non-linear functions. Did you know its functions?

In case of binary variables in the nonlinear constraint you can use Glover linearization.

Yes, Racz's advice is correct.

It is very powerful in Japanese industry systems.