The emergence of scalable highly parallel supercomputers has opened up new possibilities for modeling complex physical systems in the engineering sciences. Significant strides have been made over the past 20 years in the development, analysis, and implementation of parallel numerical methods for solution of the partial differential equations (PDEs) that govern the behavior of many of these complex physical systems. For many broad classes of simulation problems in the engineering sciences, parallel algorithms are sufficiently mature so that one may move beyond the simulation problem to optimization of systems governed by PDEs.
In contrast to the large body of work on parallel PDE solution, very little research has been conducted on parallel algorithms for optimization of PDEs. However, given the maturing state of parallel PDE solvers, time is ripe to mount a concerted effort to develop, analyze, implement, apply, and study parallel numerical methods for optimization of systems governed by PDEs or "simulation-based optimization."
Parallel algorithms for solving large-scale optimization problems governed by complex PDE systems will be developed. Efforts will focus on addressing two barriers that arise in very large scale optimization problems: large numbers of constraints and large numbers of decision variables. For the former, interior point methods will be developed and to address complexity stemming from growth in decision variables; tailor reduced- and full-space Newton-Krylov methods for the optimality system will be developed, with several choices for preconditioners including those based on infinite dimensional approximations of the reduced Hessian. The optimization methods will be implemented on highly parallel supercomputers, and applied to several challenging problems in engineering science, including inverse problems in seismic wave propagation and optimal design/control of biomedical devices. ***
