Global Optimization

Applying a global optimisation algorithm to Fund of Hedge Funds portfolio optimisation

  • Bernard Minsky
  • M Obradovic
  • Qi Tang
  • Rishi Thapar
    • Categories Applications - OR and Management Sciences, Finance and Economics, Global Optimization Tags , , ,

    Portfolio optimisation for a Fund of Hedge Funds (“FoHF”) has to address the asymmetric, non-Gaussian nature of the underlying returns distributions. Furthermore, the objective functions and constraints are not necessarily convex or even smooth. Therefore traditional portfolio optimisation methods such as mean-variance optimisation are not appropriate for such problems and global search optimisation algorithms could … Read more

    GRASP with path relinking heuristics for the antibandwidth problem

  • Abraham Duarte
  • Mauricio G.C. Resende
  • Ricardo M.A. Silva
  • Rafael Martí
    • Categories 0-1 Programming, Meta Heuristics, Stochastic Approaches Tags , , , , ,

    This paper proposes a linear integer programming formulation and several heuristics based on GRASP and path relinking for the antibandwidth problem. In the antibandwidth problem, one is given an undirected graph with N nodes and must label the nodes in a way that each node receives a unique label from the set {1, 2, …, … Read more

    Standard Bi-Quadratic Optimization Problems and Unconstrained Polynomial Reformulations

  • Immanuel M. Bomze
  • Liqun Qi
  • Chen Ling
  • Xinzhen Zhang
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory Tags , , , ,

    A so-called Standard Bi-Quadratic Optimization Problem (StBQP) consists in minimizing a bi-quadratic form over the Cartesian product of two simplices (so this is different from a Bi-Standard QP where a quadratic function is minimized over the same set). An application example arises in portfolio selection. In this paper we present a bi-quartic formulation of StBQP, … Read more

    Facial reduction algorithms for conic optimization problems

  • Masakazu Muramatsu
  • Hayato Waki
    • Categories Convex Optimization, Global Optimization Theory, Linear, Cone and Semidefinite Programming Tags ,

    To obtain a primal-dual pair of conic programming problems having zero duality gap, two methods have been proposed: the facial reduction algorithm due to Borwein and Wolkowicz [1,2] and the conic expansion method due to Luo, Sturm, and Zhang [5]. We establish a clear relationship between them. Our results show that although the two methods … Read more

    Machine Learning for Global Optimization

  • Andrea Cassioli
  • David Di Lorenzo
  • Marco Locatelli
  • Fabio Schoen
  • Marco Sciandrone
    • Categories Data-Mining, Global Optimization Tags , , ,

    In this paper we introduce the LeGO (Learning for Global Optimization) approach for global optimization in which machine learning is used to predict the outcome of a computationally expensive global optimization run, based upon a suitable training performed by standard runs of the same global optimization method. We propose to use a Support Vector Machine … Read more

    Old Wine in a New Bottle: The MILP Road to MIQCP

  • Samuel Burer
  • Anureet Saxena
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Global Optimization Theory Tags , , ,

    This paper surveys results on the NP-hard mixed-integer quadratically constrained programming problem. The focus is strong convex relaxations and valid inequalities, which can become the basis of efficient global techniques. In particular, we discuss relaxations and inequalities arising from the algebraic description of the problem as well as from dynamic procedures based on disjunctive programming. … Read more

    Nonlinear Integer Programming

  • Raymond Hemmecke
  • Matthias Köppe
  • Jon Lee
  • Robert Weismantel
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Tags

    Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic.  The primary goal is … Read more

    An algorithmic framework for MINLP with separable non-convexity

  • Claudia D'Ambrosio
  • Jon Lee
  • Andreas Wächter
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Tags , , , ,

    Global optimization algorithms, e.g., spatial branch-and-bound approaches like those implemented in codes such as BARON and COUENNE, have had substantial success in tackling complicated, but generally small scale, non-convex MINLPs (i.e., mixed-integer nonlinear programs having non-convex continuous relaxations). Because they are aimed at a rather general class of problems, the possibility remains that larger instances … Read more

    On convex relaxations of quadrilinear terms

  • Sonia Cafieri
  • Jon Lee
  • Leo Liberti
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Tags , , , , , , ,

    The best known method to find exact or at least epsilon-approximate solutions to polynomial programming problems is the spatial Branch-and-Bound algorithm, which rests on computing lower bounds to the value of the objective function to be minimized on each region that it explores. These lower bounds are often computed by solving convex relaxations of the … Read more

    Continuous GRASP with a local active-set method for bound-constrained global optimization

  • Ernesto G. Birgin
  • Mauricio G.C. Resende
  • Ricardo M. A. Silva
  • Erico M. Gozzi
    • Categories Global Optimization, Stochastic Approaches Tags , , , , ,

    Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic – based on the CGRASP and GENCAN methods – for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP-GENCAN … Read more