Senjuti

My Bad... I used one more notation : P(Tj) = P(j) (hope that clears up your confusion) Maximize, sum(j=1..z)[P(j) * mult(i=1..m)[ai * pij + (1-ai)*(1-pij)]] s.t. there would be given values for pijs and P(j)s thanks

It is a computer science problem.. More precisely this is what the problem wants to do: Naive Bayes Classifier is a probabilistic classifier which is based on Bayes Theorem and work under the assumption of independence between the variables. Without going into too much details of the actual problem ( since it is a database related problem and I have to use lots of jargon We want to maximize this objective function which is based on Naive Bayes Classifier: sum(j=1..z) [P(Tj | a1, a2......,am) ] Applying Bayes Theorem P(Tj | a1, a2......,am) = P(j) * mult(i=1..m)[P(ai | j)] Therefore, the objective function is : sum(j=1..z)[P(j) * mult(i=1..m)[P(ai | j)]] Now, a1, a2,...,am are m boolean variables and can have values 0 or 1. Now, let pij1 = P(ai=1 | j) and pij0 = P(ai=0 | j) also, pij1 + pij0 = 1 Therefore, I rewrite the objective function as follows: Maximize, sum(j=1..z)[P(j) * mult(i=1..m)[ai * pij1 + (1-ai)*(pij0)]] =sum(j=1..z)[P(j) * mult(i=1..m)[ai * pij1 + (1-ai)*(1-pij1)]] objective function, Maximize, sum(j=1..z)[P(j) * mult(i=1..m)[ai * pij + (1-ai)*(1-pij)]] (just replacing pij1 with pij) we can not consider constraints like, a1 = 1, if p11 >1/2, a1 = 1, if p12>1/2, . . . . a1= 1, if p1z>1/2. If there was no outer loop (the sum loop, which runs from 1..z), I could add constraints as you suggested and could solve the problem easily. appreciate your time.. Thanks!

Thanks... However, here is the problem: first of all pij's can not be 1 considering my application. But let's say, I consider this kind of constraints. such as, if pij > 1/2 , ai = 1. This is also not possible, cause the outer loop (sum) runs from j= 1..., z, and it would be infeasible to consider constraints like this: if p11 > 1/2 , a1 = 1 p12 > 1/2 , a1 = 1 .. p1z > 1/2, a1 = 1

thanks, the objective function is horrendous.. How to solve this efficiently?

thanks Pijs are probabilities... 0<Pij<1 I wonder which method to use to solve this.. since the objective function is horrendous... Also is there any approximation possible for such functions?

I need to solve this multi variable optimization problem of the following form Objective function: Maximize Sum(j=1...z)[Mult(i=..m)[ai*Pij + (1-ai)(1-Pij)]] here (a1, a2,...,am) are m boolean variables, can have values only 0 or 1. Can anyone please help? I need to know which method can be used to solve this optimization. I will also have a set of constraints which I am not writing down there. Finally, since this objective function seems to have a very high degree in m, which (numerical)approximation method could be used to solve such a function approximately? Appreciate your help.