## Optimization of Cost Functions that Are Defined on the Solution of Differential Algebraic Equations

Michael Wetter^{1}, Van P. Carey^{2}, and Frederick C. Winkelmann^{3}

(Professor Elijah Polak)

(DOE) DE-AC03-76SF00098 and (NSF) ECS-9900985

We are interested in the optimization of a cost function that is evaluated by a thermal building simulation program. Such programs solve a complex system of differential algebraic equations, and can nowadays only be optimized heuristically.

We developed a generalized pattern search method with adaptive precision function evaluations that uses coarse approximations to the cost function in the early iterations, with the approximation precision controlled by a test. Such an approach leads to substantial time savings, and the precision control guarantees that the optimization converges to a stationary point of the infinite precision cost function.

However, implementing the precision control requires knowledge of an error bound function which is hard to obtain for thermal building simulation programs.
Therefore, we currently develop simulation models that allow us to obtain such an error bound function, and that reduce computation time for the optimization significantly.

In parallel to the above optimization method, we develop a smoothing method that will allow using existing simulation programs for optimization with guaranteed convergence properties.

^{1}Graduate Student (non-EECS), LBNL, EETD, Simulation Research Group

^{2}Outside Adviser (non-EECS)

^{3}Outside Adviser (non-EECS), LBNL, EETD, Simulation Research Group

More information (http://www.me.berkeley.edu/~mwetter) or

Send mail to the author : (mwetter@lbl.gov)

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