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Jorge Nocedal Project I: Interior Methods for MPECS

This project explores various aspects of interior methods and preconditioners in optimization. Key focuses include minimal adaptations for MPECS, L1 formulations, and interfacing with interior methods, coupled with theoretical guarantees and applications in finance and traffic. Additionally, we delve into constrained optimization through preconditioners for related systems and explore derivative-free optimization methods. The role of commercial software like KNITRO and student versions is also discussed, highlighting research in optimization and innovative methods for robust problem-solving.

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Jorge Nocedal Project I: Interior Methods for MPECS

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  1. Jorge NocedalProject I: Interior Methods for MPECS With Gabo and Sven • Minimal adaptation (no changes to IP) • L1 formulation (Mihai) • Update penalty parameter • Interfacing with Interior Method • Theoretical guarantees • Applications in finance, traffic (?)

  2. Project II: preconditioners for Constrained optimization • With Long Hei • Preconditioners for related systems Aix= • Block preconditioners • Preconditioners for interior methods using an explicit null space basis Z (with Nick Gould) • PDE optimization- with Boulder (Cai, Byrd, Prudencio)

  3. Project III: Derivative-free optimization • With …? • Quadratic models • Least-norm update (Powell) • Robustness in the presence of noise • Convergence analysis • Exploring updating choices

  4. Miscellaneous final thoughts • Beyond active and interior methods… • KNITRO’s development (Ziena) • Like Snopt, Minos, Loqo for commercial use • Free student version • Development vs Research • Commercial face: Bob Fourer, Rick Dean • Innovative research: SBIR

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