A reformulation framework for global optimization

    Forskningsoutput: TidskriftsbidragArtikelVetenskapligPeer review

    14 Citeringar (Scopus)

    Sammanfattning

    In this paper, we present a global optimization method for solving nonconvex mixed integer nonlinear programming (MINLP) problems. A convex overestimation of the feasible region is obtained by replacing the nonconvex constraint functions with convex underestimators. For signomial functions single-variable power and exponential transformations are used to obtain the convex underestimators. For more general nonconvex functions two versions of the so-called αBB-underestimator, valid for twice-differentiable functions, are integrated in the actual reformulation framework. However, in contrast to what is done in branch-and-bound type algorithms, no direct branching is performed in the actual algorithm. Instead a piecewise convex reformulation is used to convexify the entire problem in an extended variable-space, and the reformulated problem is then solved by a convex MINLP solver. As the piecewise linear approximations are made finer, the solution to the convexified and overestimated problem will form a converging sequence towards a global optimal solution. The result is an easily-implementable algorithm for solving a very general class of optimization problems.
    OriginalspråkOdefinierat/okänt
    Sidor (från-till)115–141
    TidskriftJournal of Global Optimization
    Volym57
    Utgåva1
    DOI
    StatusPublicerad - 2013
    MoE-publikationstypA1 Tidskriftsartikel-refererad

    Citera det här