TITLE: Distributed and coordinated optimization motivated by multidisciplinary nonconvex multiobjective optimization

SPEAKER: Brian Dandurand

ABSTRACT:

The needs of distributed solution approaches to decomposable nonconvex multiobjective optimization problems motivate the study of augmented Lagrangian coordination (ALC) methods and Gauss-Seidel methods from single objective optimization. The application of certain scalarization techniques to a nonconvex, vector-valued objective function results in a reformulated single objective problem (RSOP) whose objective function may not preserve certain properties assumed in Gauss-Seidel approaches such as the alternating direction method of multipliers (ADMM). The block coordinate descent method (BCD) is considered as an alternative distributed optimization approach. While BCD requires that the constraints possess a certain decomposable structure, the formulation of the RSOP as a decomposable problem may require the introduction of extra variables and extra nondecomposable constraints. Thus, an ALC approach such as the method of multipliers must be integrated with BCD, and a corresponding analysis of such an integrated approach is warranted. 

In this presentation, a brief introduction to these concepts will be provided. Then state-of-art results for BCD and ALC methods are provided and compared with those for ADMM. A BCD coordination (BCDCoor) method consisting of an integration of BCD and ALC methods is stated as an alternative to ADMM for solving nonconvex RSOPs with nonseparable objective functions. A convergence analysis of solution-multiplier pair sequences generated by BCDCoor requires certain extensions to the state-of-art results for BCD and ALC methods. These required extensions are described, and current contributions to this end are discussed briefly.