Applications – OR and Management Sciences

What Shape is your Conjugate? A Survey of Computational Convex Analysis and its Applications

  • Yves Lucet
    • Categories Applications - OR and Management Sciences, Convex Optimization Tags , , , , , ,

    Computational Convex Analysis algorithms have been rediscovered several times in the past by researchers from different fields. To further communications between practitioners, we review the field of Computational Convex Analysis, which focuses on the numerical computation of fundamental transforms arising from convex analysis. Current models use symbolic, numeric, and hybrid symbolic-numeric algorithms. Our objective is … Read more

    A Log-Robust Optimization Approach to Portfolio Management

  • Ban Kawas
  • Aurelie Thiele
    • Categories Finance and Economics, Robust Optimization Tags , ,

    In this paper we present a robust optimization approach to portfolio management under uncertainty that (i) builds upon the well-established Lognormal model for stock prices while addressing its limitations, and (ii) incorporates the imperfect knowledge on the true distribution of the continuously compounded rates of return, i.e., the increments of the logarithm of the stock … Read more

    Robust Efficient Frontier Analysis with a Separable Uncertainty Model

  • Stephen Boyd
  • Seung-Jean Kim
    • Categories Convex Optimization, Finance and Economics, Robust Optimization Tags , , , , , , ,

    Mean-variance (MV) analysis is often sensitive to model mis-specification or uncertainty, meaning that the MV efficient portfolios constructed with an estimate of the model parameters (i.e., the expected return vector and covariance of asset returns) can give very poor performance for another set of parameters that is similar and statistically hard to distinguish from the … Read more

    A Minimax Theorem with Applications to Machine Learning, Signal Processing, and Finance

  • Stephen Boyd
  • Seung-Jean Kim
    • Categories Convex Optimization, Finance and Economics, Robust Optimization Tags , , , ,

    This paper concerns a fractional function of the form $x^Ta/\sqrt{x^TBx}$, where $B$ is positive definite. We consider the game of choosing $x$ from a convex set, to maximize the function, and choosing $(a,B)$ from a convex set, to minimize it. We prove the existence of a saddle point and describe an efficient method, based on … Read more

    Sample Average Approximation of Expected Value Constrained Stochastic Programs

  • Shabbir Ahmed
  • W. Wang
    • Categories Finance and Economics, Stochastic Programming

    We propose a sample average approximation (SAA) method for stochastic programming problems involving an expected value constraint. Such problems arise, for example, in portfolio selection with constraints on conditional value-at-risk (CVaR). Our contributions include an analysis of the convergence rate and a statistical validation scheme for the proposed SAA method. Computational results using a portfolio … Read more

    Optimal solutions for unrelated parallel machines scheduling problems using convex quadratic reformulations

  • M.-C. Plateau
  • Yasmin Rios-Solis
    • Categories Applications - OR and Management Sciences, Quadratic Programming, Scheduling Tags , ,

    In this work, we take advantage of the powerful quadratic programming theory to obtain optimal solutions of scheduling problems. We apply a methodology that starts, in contrast to more classical approaches, by formulating three unrelated parallel machine scheduling problems as 0–1 quadratic programs under linear constraints. By construction, these quadratic programs are non-convex. Therefore, before … Read more

    The Transportation Paradox Revisited

  • Sverre Storøy
    • Categories Linear Programming, Transportation

    The transportation paradox is related to the classical transportation problem. For certain instances of this problem an increase in the amount of goods to be transported may lead to a decrease in the optimal total transportation cost. Even though the paradox has been known since the early days of linear programming, it has got very … Read more

    Single-layer Cuts for Multi-layer Network Design Problems

  • Georg Baier
  • Arie M.C.A. Koster
  • Sebastian Orlowski
  • Thomas Engel
  • Christian Raack
    • Categories Branch and Cut Algorithms, Cutting Plane Approaches, Telecommunications Tags , , ,

    We study a planning problem arising in SDH/WDM multi-layer telecommunication network design. The goal is to find a minimum cost installation of link and node hardware of both network layers such that traffic demands can be realized via grooming and a survivable routing. We present a mixed-integer programming formulation that takes many practical side constraints … Read more

    Single Item Lot-Sizing with Nondecreasing Capacities

  • Yves Pochet
  • Laurence A. Wolsey
    • Categories (Mixed) Integer Linear Programming, Polyhedra, Production and Logistics Tags , , ,

    We consider the single item lot-sizing problem with capacities that are non-decreasing over time. When the cost function is i) non-speculative or Wagner-Whitin (for instance, constant unit production costs and non-negative unit holding costs), and ii) the production set-up costs are non-increasing over time, it is known that the minimum cost lot-sizing problem is polynomially … Read more