# Mathematics Colloquia and Seminars

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### Optimization and Design of Complex Engineering Systems using High Performance Computing

**Special Events**

Speaker: | Cosmin Petra, Lawrence Livermore National Laboratory |

Location: | 2112 MSB |

Start time: | Thu, Mar 9 2017, 3:10PM |

Optimal design, planning, and operation of nationally critical engineering systems such as the energy infrastructure and additive manufacturing require solving large-scale mathematical optimization problems that are governed by physics models and involve multiple sources of uncertainty. In many real-world applications, these optimization problems reach extreme sizes to require high-performance computing (HPC) algorithms, stemming from the necessity to use high-fidelity physics, accurate uncertainty characterizations and to optimize over geographically large areas and/or at detailed time resolutions.

In this talk, I will focus on algorithmic work in the direction of parallel quasi-Newton interior-point methods for PDE- and DAE-constrained optimization problems. We will cover a quasi-Newton method that uses structured secant updates to make use of existing, but incomplete second-order derivative information. We will start by discussing the motivating applications (e.g., structural topology optimization and security constrained optimal electrical power flow) and then proceed to algorithm design considerations and convergence analysis. We will also discuss the parallelization of the linear algebra of the quasi-Newton interior-point method and present preliminary HPC performance results of the implementation on structural topology optimization problems.

I will close my talk with an overview of ongoing synergies at Lawrence Livermore National Laboratory in computational and applied mathematics and touch on career opportunities at national labs.

A career Q&A for graduate students will follow the presentation.