Allen Holder presents special Mechanical and Industrial Engineering seminar

Holder will review a couple of classic examples to highlight the central modeling themes and then adapt the robust paradigm to a popular problem in computational biology called flux balance analysis (FBA). Previous FBA models have been linear or quadratic and have assumed a static relationship between a cell's environment and its growth rate. This assumption is doubtful, and the static model has to be extended to a robust counterpart that accounts for the inherit uncertainty in individual variation. The robust model advances traditional FBA's validity with regard to its scientific goals since it removes the menacing shortcoming of ignoring dynamics. The biological setting leads naturally to questions about if, and if so how, solutions to robust models converge to their static counterparts as uncertain parameters become certain. One of these results argues that static solutions are robust solutions if the variation is appropriately restricted. With regard to engineering designs, this means that optimal designs created under static conditions are indeed robust under some restricted set of parametric variation.

 

Holder says many of the engineering models are solved efficiently with modern second-order cone solvers. However, these solvers have been unsuccessful at solving the robust FBA models. The exact reason for this failure is unknown, and Holder is working to enhance the numerical stability of the optimizers. He will point to some of suspicions about why the solvers have been unfaithful in the biological setting. If researchers are successful in rectifying the numerics, then
the engineering applications will gain more trustworthy solvers. The robust FBA problem can be remodeled to make use of a different solver, which has proven itself worthy of the computational task.