Optimization Problems with Inequality Constraints or a Non-Differentiable Objective: Parallel Algorithms Development and Their Applications(2/2)

Project Details

Description

The goal of this proposed project is to develop the parallel, scalable, efficient solution algorithms for solving large-scale nonlinear system of equations arising from constrained optimization problems. We are particularly interested in the problem with inequality constraints and non-differentiable objective functions involved. Such problems represent a broad range of applications in computational sciences and engineerings, such as flow control problems, the dogleg trajectory optimization problems in the space mission, l1- regularized least-squares problems in the statistics and data sciences. Addition to the high dimensionality, such characteristics make the optimization problems more challenging to solve. The semi-smooth Newton method is one of the most popular methods for the non-smooth system also suffer from the convergence issue when the nonlinearity of the system is not well balanced. Nonlinear preconditioning technique provides alternative other than globalization techniques, e.g., linesearch or trust region not only to enhance the robustness of Newton type method but also to accelerate the convergence of some Krylov subspace method In this project, we will study a variety of nonlinear iterative methods as preconditioners for semi-smooth Newton algorithms and nonlinear Krylov subspace method, such as nonlinear Generalized Minimal Residuals MRES (GMRES) method. This includes nonlinear elimination method, which has been successfully applied to some difficult PDE problems with strong local nonlinearity with applications in computational fluid dynamics and flow control problems and others. We also consider the decoupled algorithms, namely the method of penalty method, the method of Lagrange multipliers, and the Alternating direction method and Method of Multipliers (ADDM). All the algorithms considered will be implemented on the top of Portable, Extensible, Toolkits for Scientific computation (PETSc) and will be tested on the different state-of-the-art computer platforms, including a cluster of PCs, the multicore system, and hybrid CPU/GPU system and its parallel performance on these platforms will be studied. Hopefully, this PETSc-based scientific package can be beneficial to scientific community and industry.
StatusActive
Effective start/end date1/08/2031/01/22

UN Sustainable Development Goals

In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This project contributes towards the following SDG(s):

  • SDG 11 - Sustainable Cities and Communities
  • SDG 12 - Responsible Consumption and Production
  • SDG 17 - Partnerships for the Goals

Keywords

  • Nonlinear preconditioning
  • Constrained optimization
  • semi-smooth Newton
  • NGMRES
  • Nonlinear elimination
  • ADMM
  • flow control
  • l1norm regularized least squares problem
  • dogleg trajectory

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