Re: fmincon

Thanks for response,
You are right,the size of the rectangles is limmited by the following:

My description was like there is only one union of several rectangles,actually there are two such unions.
Each one grasping its own data distribution defined by its covariance matrix.
The goal is to lead the product of double integrals (of probability density ,each over its union) to maximum. Two these regions constraint as follows:
The mean of any two points (one point belongs to first union and second point to second union) must fall inside some region in the plane. The reason I work with rectangles is that it's simple to integrate over them and the most important: due to convexity of rectangle it's sufficient to check the constraints only for verteces of rectangle i.e. if i take two rectangles (one from first union and the second one from the second union) to check the mean of any two points is inside some region i just check the mean of appropriate verteces.

I'm rather don't catch something but it's strange: check the point is inside rectangle is implemented with two simple linear constraints but to constrain the opposite is something not so simple.

Thanks,
Alex


"Matt " <mjacobson.removethis@xxxxxxxxxxxxx> wrote in message <gda89o$opb$1@xxxxxxxxxxxxxxxxxx>...
"Alexander Blumin" <bluminalex@xxxxxxxxx> wrote in message <gd823h$836$1@xxxxxxxxxxxxxxxxxx>...
Hi guys,

I'm working with fmincon on the following optimization problem:

Given a set of rectangles and bivariate normal distribution
i'd like to find the 'best' rectangles position and size.
'Best' here it means the resulted rectangle's union grasp more probability.(My objective function is actually a double integral over union of these recntangles).

Now finally the problem: At this stage i'd like to require a disjoint rectangles in my constraints enequalities.
I don't find a way to do it. Simple way to say rectnagles does not intersect is to say no vertex of one is inside another one. Now to say point outside of rectangle is to require point.x outside the x range of recntangle OR point.y outside the y range of recntangle. I don't know how to implement this OR. This is logical and isn't continuous constraint,isn't it?

Any help or thoughts are highly appriciated.

Thank,
Alex


I'm assuming there are constraints on the sizes of your rectangles? Otherwise, the optimal solution is obviously just an infinite sized rectangle that covers all of R^2.

It might help to know what those constraints are.

It's pretty clear that in an optimal solution, the rectangles must all be touching each other and be as close as possible to the mode of the normal distribution.

You might therefore be able to reduce the problem to the optimization of a single closed shape...





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