Novel Decomposition and Active-Set Techniques Enabling Scalable Computational Frameworks for Large-Scale Nonlinear Optimization Problems

Project: Research project

Project Details

Description

In many real-life situations, decisions have to be made in the absence of perfect information, either due to the lack of reliable data or due to unforeseen events. Many practical algorithms in the domain of stochastic optimization address this situation by considering a large number of potential scenarios in problem formulations. This results in instances that are too large to be solved directly and that have to be tackled with decomposition methods.
The investigator proposes to create novel decomposition frameworks for nonconvex continuous optimization problems, together with theory, algorithms, and software, that do not require strong modeling assumptions such as linearity, that are scalable from multi-core to high-performance computing environments, and that are more flexible than existing methods. The proposed methodology is fundamentally different from existing approaches. Its master problems integrate the nonlinear responses of the subproblems directly, instead of building an approximation over time. This makes it possible to utilize reliable and existing nonlinear optimization software and to achieve fast local convergence rates.
The fi�rst part of the research program focuses on partially separable problems. These arise, for
example, in the context of stochastic multi-stage problems or loosely connected networks. The key
ingredient is a smoothing technique that overcomes the predicament that the optimal subproblem
solutions are not differentiable functions of the master problem variables. Further challenges include the proper treatment of spurious degeneracy and the use of inexact subproblem solutions to speed up the convergence. The second part extends the methodology to stochastic continuous bi-level problems, a challenging problem class for which no practical scalable decomposition algorithms have been developed yet, even for the linear case. Throughout the project, the algorithms will be tested on realistic problems in power systems.
StatusNot started
Effective start/end date9/1/208/31/23

Funding

  • National Science Foundation (DMS-2012410)

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