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

    The Delivery Man Problem with Time Windows

  • Jean-François Cordeau
  • Géraldine Heilporn
  • Gilbert Laporte
    • Categories (Mixed) Integer Linear Programming Tags , , , ,

    In this paper, a variant of the Traveling Salesman Problem with Time Windows is considered, which consists in minimizing the sum of travel durations between a depot and several customer locations. Two mixed integer linear programming formulations are presented for this problem: a classical arc flow model and a sequential assignment model. Several polyhedral results … Read more

    On the Central Paths and Cauchy Trajectories in Semidefinite Programming

  • Julio López
  • Héctor Ramírez
    • Categories Semi-definite Programming Tags , , , ,

    In this work, we study the properties of central paths, defined with respect to a large class of penalty and barrier functions, for convex semidefinite programs. The type of programs studied here is characterized by the minimization of a smooth and convex objective function subject to a linear matrix inequality constraint. So, it is a … Read more

    All roads lead to Newton: Feasible second-order methods for equality-constrained optimization

  • Pierre-Antoine Absil
  • Ben Andrews
  • Robert Mahony
  • Jochen Trumpf
    • Categories Constrained Nonlinear Optimization

    This paper considers the connection between the intrinsic Riemannian Newton method and other more classically inspired optimization algorithms for equality-constrained optimization problems. We consider the feasibly-projected sequential quadratic programming (FP-SQP) method and show that it yields the same update step as the Riemannian Newton, subject to a minor assumption on the choice of multiplier vector. … Read more

    Risk-Averse Two-Stage Stochastic Linear Programming: Modeling and Decomposition

  • Naomi Miller
  • Andrzej Ruszczyński
    • Categories Stochastic Programming Tags , ,

    We formulate a risk-averse two-stage stochastic linear programming problem in which unresolved uncertainty remains after the second stage. The objective function is formulated as a composition of conditional risk measures. We analyze properties of the problem and derive necessary and sufficient optimality conditions. Next, we construct two decomposition methods for solving the problem. The first … Read more

    Compressed Sensing: How sharp is the RIP?

  • Jeffrey Blanchard
  • Coralia Cartis
  • Jared Tanner
    • Categories Applications - Science and Engineering Tags , , ,

    Consider a measurement matrix A of size n×N, with n < N, y a signal in R^N, and b = Ay the observed measurement of the vector y. From knowledge of (b,A), compressed sensing seeks to recover the k-sparse x, k < n, which minimizes ||b-Ax||. Using various methods of analysis — convex polytopes, geometric … Read more

    Phase Transitions for Greedy Sparse Approximation Algorithms

  • Jeffrey Blanchard
  • Coralia Cartis
  • Jared Tanner
  • Andrew Thompson
    • Categories Applications - Science and Engineering Tags , , ,

    A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many such algorithms have now been proven using the ubiquitous Restricted Isometry Property (RIP) [9] to have optimal-order uniform recovery guarantees. However, it is … Read more

    Finite Disjunctive Programming Characterizations for General Mixed-Integer Linear Programs

  • Binyuan Chen
  • Simge Küçükyavuz
  • Suvrajeet Sen
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags , , ,

    In this paper, we give a finite disjunctive programming procedure to obtain the convex hull of general mixed-integer linear programs (MILP) with bounded integer variables. We propose a finitely convergent convex hull tree algorithm which constructs a linear program that has the same optimal solution as the associated MILP. In addition, we combine the standard … Read more

    Building a completely positive factorization

  • Immanuel M. Bomze
    • Categories Linear, Cone and Semidefinite Programming Tags , ,

    Using a bordering approach, and building upon an already known factorization of a principal block, we establish sufficient conditions under which we can extend this factorization to the full matrix. Simulations show that the approach is promising also in higher dimensions. CitationPreprint, Univ.of Vienna (2017), submittedArticleDownload View PDF

    A new LP algorithm for precedence constrained production scheduling

  • Daniel Bienstock
  • Mark Zuckerberg
    • Categories Combinatorial Optimization, Integer Programming, Linear, Cone and Semidefinite Programming Tags , ,

    We present a number of new algorithmic ideas for solving LP relaxations of extremely large precedence constrained production scheduling problems. These ideas are used to develop an implementation that is tested on a variety of real-life, large scale instances; yielding optimal solutions in very practicable CPU time. CitationUnpublished. Columbia University, BHP Billiton, August 2009.ArticleDownload View … Read more