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An optimization problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110448] An optimization problem
  • From: pratip <pratip.chakraborty at gmail.com>
  • Date: Sat, 19 Jun 2010 07:46:23 -0400 (EDT)

Dear Group Members,

I have a function
Objective[ c_, p_, t_, l1_, l2_, MasterDisrcrit_,MasterPoints : {{_,
_} ..}] that gives list of three numbers as output.

Now my optimization problem is something like the following

Max Objective[c,p,t,l1,l2,dat][[1]] with constraints as below
for the parameters {c,p,t,l1,l2}

cmin<c<cmax,...,l2min<l2<l1min

for the list of n pairs of 2D points "dat" with pattern MasterPoints :
{{_, _} ..}
If dat={dat[[1]],...,dat[[n]]} (Assume n to be even) then the
constraints are

for all First[dat[[1]]],...,First[dat[[n/2]]] they are bounded by
k1<First[dat[[i]]]<k2
for all Last[dat[[1]]],...,Last[dat[[n/2]]] they are bounded by
g1<Last[dat[[i]]]<g2

last constraints are

O21<Objective[c,p,t,l1,l2,dat][[2]] <O22
O31<Objective[c,p,t,l1,l2,dat][[3]] <O32

Now I see mathematica has problem to solve such optimization problem.
Keeping a variable of the pattern like MasterPoints : {{_, _} ..} this
is necessary because I can increase or decrease the number of 2D
points whenever needed and In general we will have more than 40 such
2D points. So writing them separately in the function definition is no
solution. Mathematica complains with FindMaximum that no constraints
can be used on the list of 2D points "dat".

I hope some of you have got some experience with this type of problem
scenario.

Regards,

Pratip


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