Structure Exploiting Interior Point Methods

TL;DR

This paper presents a parallel interior point method that leverages problem structure and high-performance computing to efficiently solve large-scale nonlinear optimization problems, especially in power grid applications.

Contribution

It introduces a structure-exploiting parallel interior point method with a focus on scalable sparse linear algebra for large-scale nonlinear optimization.

Findings

Effective parallel implementation for large-scale problems

Improved solution times for power grid optimization

Demonstrated scalability with high-performance computing

Abstract

Interior point methods are among the most popular techniques for large scale nonlinear optimization, owing to their intrinsic ability of scaling to arbitrary large problem sizes. Their efficiency has attracted in recent years a lot of attention due to increasing demand for large scale optimization in industry and engineering. A parallel interior point method is discussed that exploits the intrinsic structure of large-scale nonlinear optimization problems so that the solution process can employ massively parallel high-performance computing infastructures. Since the overall performance of interior point methods relies heavily on scalable sparse linear algebra solvers, particular emphasis is given to the underlying algorithms for the distributed solution of the associated sparse linear systems obtained at each iteration from the linearization of the optimality conditions. The interior point algorithm is implemented in a object-oriented parallel IPM solver and applied for the solution of large scale optimal control problems solved in a daily basis for the secure transmission and distribution of electricity in modern power grids.