deterministic global optimization

BASBL: Branch-And-Sandwich BiLevel solver I. Theoretical advances and algorithmic improvements

  • Claire S. Adjiman
  • Remigijus Paulavicius
    • Categories Global Optimization Theory Tags , ,

    In this paper, we consider the global solution of bilevel programs involving nonconvex functions. We present algorithmic improvements and extensions to the recently proposed deterministic Branch-and-Sandwich algorithm (Kleniati and Adjiman, J. Glob. Opt. 60, 425–458, 2014), based on the theoretical results and heuristics. Choices in the way each step of the Branch-and-Sandwich algorithm is tackled, … Read more

    Optimal Design of Electrical Machines: Mathematical Programming Formulations

  • Sonia Cafieri
  • Leo Liberti
  • Frédéric Messine
  • Bertrand Nogarède
    • Categories Constrained Nonlinear Optimization, Global Optimization Applications, Multidisciplinary Design Optimization Tags , , , , , , ,

    The optimal design of electrical machines can be mathematically modeled as a mixed-integer nonlinear optimization problem. We present six variants of such a problem, and we show, through extensive computational experiments, that, even though they are mathematically equivalent, the differences in the formulations may have an impact on the numerical performances of a local optimization … Read more

    Global minimization using an Augmented Lagrangian method with variable lower-level constraints

  • Ernesto G. Birgin
  • Christodoulos A. Floudas
  • José Mario Martínez
    • Categories Global Optimization Tags , , ,

    A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration the method requires the $\varepsilon$-global minimization of the Augmented Lagrangian with simple constraints. Global convergence to an $\varepsilon$-global minimizer of the original problem is proved. The subproblems are solved using the $\alpha$BB … Read more