Griffin D. Kent

Bilevel optimization with a multi-objective lower-level problem: Risk-neutral and risk-averse formulations

  • Tommaso Giovannelli
  • Griffin D. Kent
  • Luis Nunes Vicente
    • Categories Data-Mining, Multi-Criteria Optimization, Stochastic Programming Tags , , ,

    In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the deterministic case and have never been studied from a stochastic approximation viewpoint despite the recent advances in stochastic methods for single-level, bilevel, and multi-objective … Read more

    Inexact bilevel stochastic gradient methods for constrained and unconstrained lower-level problems

  • Tommaso Giovannelli
  • Griffin D. Kent
  • Luis Nunes Vicente
    • Categories Data-Mining, Nonlinear Optimization, Stochastic Programming Tags , , ,

    Two-level stochastic optimization formulations have become instrumental in a number ofmachine learning contexts such as continual learning, neural architecture search, adversariallearning, and hyperparameter tuning. Practical stochastic bilevel optimization problemsbecome challenging in optimization or learning scenarios where the number of variables ishigh or there are constraints. In this paper, we introduce a bilevel stochastic gradient method … Read more

    Penetration depth between two convex polyhedra: An efficient global optimization approach

  • Mark A. Abramson
  • Griffin D. Kent
  • Gavin W. Smith
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Global Optimization Applications Tags , , , ,

    During the detailed design phase of an aerospace program, one of the most important consistency checks is to ensure that no two distinct objects occupy the same physical space. Since exact geometrical modeling is usually intractable, geometry models are discretized, which often introduces small interferences not present in the fully detailed model. In this paper, … Read more