global optimization

A dimensionality reduction technique for unconstrained global optimization of functions with low effective dimensionality

  • Coralia Cartis
  • Adilet Otemissov
    • Categories Global Optimization, Stochastic Approaches Tags , , ,

    We investigate the unconstrained global optimization of functions with low effective dimensionality, that are constant along certain (unknown) linear subspaces. Extending the technique of random subspace embeddings in [Wang et al., Bayesian optimization in a billion dimensions via random embeddings. JAIR, 55(1): 361–387, 2016], we study a generic Random Embeddings for Global Optimization (REGO) framework … Read more

    On tackling reverse convex constraints for non-overlapping of unequal circles

  • Chrysanthos E. Gounaris
  • Akang Wang
    • Categories Global Optimization, Global Optimization Applications Tags , , , , ,

    We study the unequal circle-circle non-overlapping constraints, a form of reverse convex constraints that often arise in optimization models for cutting and packing applications. The feasible region induced by the intersection of circle-circle non-overlapping constraints is highly non-convex, and standard approaches to construct convex relaxations for spatial branch-and-bound global optimization of such models typically yield … Read more

    On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming

  • Maxime Gasse
  • Ambros Gleixner
  • Andrea Lodi
  • Felipe Serrano
  • Benjamin Müller
  • Gonzalo Muñoz
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Nonlinear Optimization Tags ,

    The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solver can often successfully handle a moderate presence of nonconvexities, which opens … Read more

    Visible points, the separation problem, and applications to MINLP

  • Felipe Serrano
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Global Optimization Tags , , , ,

    In this paper we introduce a technique to produce tighter cutting planes for mixed-integer non-linear programs. Usually, a cutting plane is generated to cut off a specific infeasible point. The underlying idea is to use the infeasible point to restrict the feasible region in order to obtain a tighter domain. To ensure validity, we require … Read more

    A Method for Convex Black-Box Integer Global Optimization

  • Jeffrey Larson
  • Sven Leyffer
  • Prashant Palkar
  • Stefan M. Wild
    • Categories Convex Optimization Tags , , ,

    We study the problem of minimizing a convex function on the integer lattice when the function cannot be evaluated at noninteger points. We propose a new underestimator that does not require access to (sub)gradients of the objective but, rather, uses secant linear functions that interpolate the objective function at previously evaluated points. These linear mappings … Read more

    Using two-dimensional Projections for Stronger Separation and Propagation of Bilinear Terms

  • Ambros Gleixner
  • Felipe Serrano
  • Benjamin Müller
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Nonlinear Optimization Tags , , , , , ,

    One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well- known McCormick relaxation for a product of two variables x and y over a box-constrained domain. The starting point of this paper is the fact that the convex hull of the graph of xy can be much tighter when computed over … Read more

    Escaping local minima with derivative-free methods: a numerical investigation

  • Coralia Cartis
  • Lindon Roberts
  • Oliver Sheridan-Methven
    • Categories Nonlinear Optimization Tags , ,

    We apply a state-of-the-art, local derivative-free solver, Py-BOBYQA, to global optimization problems, and propose an algorithmic improvement that is beneficial in this context. Our numerical findings are illustrated on a commonly-used test set of global optimization problems and associated noisy variants, and on hyperparameter tuning for a machine learning test set. As Py-BOBYQA is a … Read more

    On local non-global minimizers of quadratic optimization problem with a single quadratic constraint

  • Maziar Salahi
  • Akram Taati
    • Categories Global Optimization, Nonlinear Optimization Tags , , ,

    In this paper, we consider the nonconvex quadratic optimization problem with a single quadratic constraint. First we give a theoretical characterization of the local non-global minimizers. Then we extend the recent characterization of the global minimizer via a generalized eigenvalue problem to the local non-global minimizers. Finally, we use these results to derive an efficient … Read more

    Global Solutions of Nonconvex Standard Quadratic Programs via Mixed Integer Linear Programming Reformulations

  • Jacek Gondzio
  • E. Alper Yildirim
    • Categories (Mixed) Integer Linear Programming, Quadratic Programming Tags , , ,

    A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We propose two alternative mixed integer linear programming formulations. Our first formulation is based on casting a standard quadratic program … Read more

    Efficient global unconstrained black box optimization

  • Morteza Kimiaei
  • Arnold Neumaier
    • Categories Stochastic Approaches, Unconstrained Optimization Tags , , , ,

    For the unconstrained optimization of black box functions, this paper introduces a new randomized algorithm called VRBBO. In practice, VRBBO matches the quality of other state-of-the-art algorithms for finding, in small and large dimensions, a local minimizer with reasonable accuracy. Although our theory guarantees only local minimizers our heuristic techniques turn VRBBO into an efficient … Read more