actually i am willing to model a classic problem of association rule by a standard constraint optimization which can be nonlinear and non-convex too but with minimum number of constraints and optimization variables.
Dear Behrad,
Here are Links and some attached files in subject.
OPTIMIZATION WITH LINEAR COMPLEMENTARITY CONSTRAINTS
www.scielo.br/scielo.php?script=sci_arttext&pid.
Combinatorial and Integer Optimization
www.esi2.us.es/~mbilbao/combiopt.htm
Integer Optimization and the Network Models - University of Baltimore ...
home.ubalt.edu/ntsbarsh/opre640A/partIII.htm
Best regards
Dear Behrad,
What do you mean when you say "association rule"?
If It is in the sense:
---> IF THEN
A mixed integer model can be formulated with the "big-M" constraints. Considering y a binary variable, we can state:
---> >= K*y
--> >= K*(1-y)
--> * y >= 0
...
Let me know if your problem does not fit the technique explained in my answer.
Best regards
Actually your formulation is correct when the condition and consequence are available! however in association rule learning the the condition and consequence events are sets of multiple outcomes that belong to a bigger set of sample space! and the goal is to find the set of outcomes that belong to the condition in your terminology and the set of outcomes belong to consequence event!
Many years ago I had to solve nonlinear programming problems with integer variables, such as the optimal designing of finned compressed cylindrical shells in the axial direction. According to the conditions of task it was required that the number of longitudinal and transverse ribs were integers. Other parameters (wall thickness of the shell and its radius, the sizes of ribs) were could be the nonintegral variables.Was minimized the mass of the shell at the restrictions on strength, rigidity and stability. Has been used a method of random search with self-learning. We did not mix the integer and non-integer programming, and we solved the problem, as the problem of noninteger programming, followed by rounding of number of edges to integers at each step of the search and we checked affiliation of received point to the area of permissible solutions. The next step was executed out of the point found in this way, taking into account the prehistory of search. It turned not bad.
Sincerely, George Filatov
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