Month: December 2015

Strengthening the SDP Relaxation of AC Power Flows with Convex Envelopes, Bound Tightening, and Lifted Nonlinear Cuts

  • Carleton Coffrin
  • Hassan L. Hijazi
  • Pascal Van Hentenryck
    • Categories Applications - OR and Management Sciences, Constrained Nonlinear Optimization, Semi-definite Programming Tags , , ,

    This paper considers state-of-the-art convex relaxations for the AC power flow equations and introduces new valid cuts based on convex envelopes and lifted nonlinear constraints. These valid linear inequalities strengthen existing semidefinite and quadratic programming relaxations and dominate existing cuts proposed in the litterature. Together with model intersections and bound tightening, the new linear cuts … Read more

    Convex Hull Characterizations of Lexicographic Orderings

  • Warren Adams
  • Pietro Belotti
  • Ruobing Shen
    • Categories (Mixed) Integer Linear Programming, Polyhedra Tags , ,

    Given a p-dimensional nonnegative, integral vector α, this paper characterizes the convex hull of the set S of nonnegative, integral vectors x that is lexicographically less than or equal to α. To obtain a finite number of elements in S, the vectors x are restricted to be component-wise upper-bounded by an integral vector u. We … Read more

    Data-Driven Inverse Optimization with Imperfect Information

  • Grani A. Hanasusanto
  • Daniel Kuhn
  • Peyman Mohajerin Esfahani
  • Soroosh Shafieezadeh-Abadeh
    • Categories Linear, Cone and Semidefinite Programming, Robust Optimization, Stochastic Programming Tags , ,

    In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agent’s objective function that best explains a historical sequence of signals and corresponding optimal actions. We focus here on situations where the observer has imperfect … Read more

    SMART: The Stochastic Monotone Aggregated Root-Finding Algorithm

  • Damek Davis
    • Categories Convex and Nonsmooth Optimization Tags , , , , ,

    We introduce the Stochastic Monotone Aggregated Root-Finding (SMART) algorithm, a new randomized operator-splitting scheme for finding roots of finite sums of operators. These algorithms are similar to the growing class of incremental aggregated gradient algorithms, which minimize finite sums of functions; the difference is that we replace gradients of functions with black-boxes called operators, which … Read more

    Solutions of a constrained Hermitian matrix-valued function optimization problem with applications

  • Yongge Tian
    • Categories Constrained Nonlinear Optimization Tags

    Let $f(X) =\left( XC + D\right)M\left(XC + D \right)^{*} – G$ be a given nonlinear Hermitian matrix-valued function with $M = M^*$ and $G = G^*$, and assume that the variable matrix $X$ satisfies the consistent linear matrix equation $XA = B$. This paper shows how to characterize the semi-definiteness of $f(X)$ subject to all … Read more

    On the Polyhedral Structure of Two-Level Lot-Sizing Problems with Supplier Selection

  • Ayse Nur Arslan
  • Yongpei Guan
  • Jean-Philippe P. Richard
    • Categories (Mixed) Integer Linear Programming, Production and Logistics Tags , , ,

    In this paper, we study a two-level lot-sizing problem with supplier selection (LSS). This NP-hard problem arises in different production planning and supply chain management applications. We first present a dynamic programming algorithm for LSS that is polynomial when the number of plants is fixed. We use this algorithm to describe the convex hull of … Read more

    Distributionally Robust Stochastic Programming

  • Alexander Shapiro
    • Categories Robust Optimization, Stochastic Programming Tags , , , , ,

    In this paper we study distributionally robust stochastic programming in a setting where there is a specified reference probability measure and the uncertainty set of probability measures consists of measures in some sense close to the reference measure. We discuss law invariance of the associated worst case functional and consider two basic constructions of such … Read more

    Robust Nonparametric Testing for Causal Inference in Observational Studies

  • Md. Noor-E-Alam
  • Cynthia Rudin
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Data-Mining Tags , , , , ,

    We consider the decision problem of making causal conclusions from observational data. Typically, using standard matched pairs techniques, there is a source of uncertainty that is not usually quanti fied, namely the uncertainty due to the choice of the experimenter: two di fferent reasonable experimenters can easily have opposite results. In this work we present an alternative … Read more

    A framework for simultaneous aerodynamic design optimization in the presence of chaos

  • Nicolas R. Gauger
  • Stefanie Günther
  • Qiqi Wang
    • Categories Systems governed by Differential Equations Optimization Tags , , , , ,

    Integrating existing solvers for unsteady partial differential equations (PDEs) into a simultaneous optimization method is challenging due to the forward- in-time information propagation of classical time-stepping methods. This paper applies the simultaneous single-step one-shot optimization method to a reformulated unsteady PDE constraint that allows for both forward- and backward-in-time information propagation. Especially in the presence … Read more

    Application of the Laminar Navier-Stokes Equations for Solving 2D and 3D Pathfinding Problems with Static and Dynamic Spatial Constraints. Implementation and validation in Comsol Multiphysics.

  • Benjamin Ivorra
    • Categories Applications - Science and Engineering, Other Topics, Transportation

    Pathfinding problems consist in determining the optimal shortest path, or at least one path, between two points in the space. In this paper, we propose a particular approach, based on methods used in Computational Fluid Dynamics, that intends to solve such problems. In particular, we reformulate pathfinding problems as the motion of a viscous fluid … Read more