Originally posted by: SystemAdmin

[Kent said:]

I have a differential equation system. I theorize that if I make a finite difference equation system out of it, then I can solve the algebraic equation system. If the algebraic equation system contains just linear stuff, then I can solve it with LP. Has anyone done something like this with OPL?

regards
Kent
#DecisionOptimization
#OPLusingCPOptimizer

Originally posted by: SystemAdmin

[jfk said:]

Hello Kent,
I haven't heard about any project where directly OPL was used in relation with Differential Equations. What you are suggesting is an interesting idea, and I think it can definitely work. CPLEX (an LP solver) is used extensively to solve NLP problems after linearization, so it is up to the user to lienarize and then solve it. Actually many NLP solving approach is categorized as SLP or SQP, sequential linear programming or sequantial quadratic programming, respectively. In case of SLP after linearization of the nonlinear constraints and the goal function an LP problem is solved, then adjusted (the linearization may violate some constraints) to get feasible solution. The solution serves as a new "basis" to linearize the nonlinear problem again, and the process is done sequentially until a given halt criteria is satisfied. In case of SQP the general process is the same except that the goal is not linearized but made into a quadratic approximation. So instead of an LP, a QP is solved sequentially. What sort of Differential Eqautaion System do you want to solve? I mean what is the application, if any?

cheers
Ferenc
#DecisionOptimization
#OPLusingCPOptimizer

Originally posted by: SystemAdmin

[ChrisHane said:]

Hello Kent,

You may be interested in this paper by Richards et al on controlling UAVs with MILP models, http://acl.mit.edu/papers/Richards39451.pdf.

The group of authors at MIT is doing other work on trajectory control problems using math programming too.

Chris
#DecisionOptimization
#OPLusingCPOptimizer