A Class of Smooth Exact Penalty Function Methods for Optimization Problems with Orthogonality Constraints

  • Nachuan Xiao
  • Xin Liu
  • Ya-xiang Yuan
    • Categories Basic Sciences Applications, Constrained Nonlinear Optimization Tags , ,

    Updating the augmented Lagrangian multiplier by closed-form expression yields efficient first-order infeasible approach for optimization problems with orthogonality constraints. Hence, parallelization becomes tractable in solving this type of problems. Inspired by this closed-form updating scheme, we propose an exact penalty function model with compact convex constraints (PenC). We show that PenC can act as an … Read more

    MathOptInterface: a data structure for mathematical optimization problems

  • Joaquim Dias Garcia
  • Oscar Dowson
  • Miles Lubin
  • Benoit Legat
    • Categories Modeling Languages and Systems, Optimization Software Design Principles

    JuMP is an open-source algebraic modeling language in the Julia language. In this work, we discuss a complete re-write of JuMP based on a novel abstract data structure, which we call \textit{MathOptInterface}, for representing instances of mathematical optimization problems. MathOptInterface is significantly more general than existing data structures in the literature, encompassing, for example, a … Read more

    Mixed-Integer Linear Programming for Scheduling Unconventional Oil Field Development

  • Jeff Linderoth
  • James R. Luedtke
  • Fabian Rigterink
  • Akhilesh Soni
    • Categories Scheduling Tags , , ,

    The scheduling of drilling and hydraulic fracturing of wells in an unconventional oil field plays an important role in the profitability of the field. A key challenge arising in this problem is the requirement that neither drilling nor oil production can be done at wells within a specified neighborhood of a well being fractured. We … Read more

    A bundle method for nonsmooth DC programming with application to chance-constrained problems

  • Welington de Oliveira
  • Sophie Demassey
  • Paul Javal
  • Hugo Morais
  • Bhargav Swaminathan
  • Wim van Ackooij
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags

    This work considers nonsmooth and nonconvex optimization problems whose objective and constraint functions are defined by difference-of-convex (DC) functions. We consider an infeasible bundle method based on the so-called improvement functions to compute critical points for problems of this class. Our algorithm neither employs penalization techniques nor solves subproblems with linearized constraints. The approach, which … Read more

    On convex hulls of epigraphs of QCQPs

  • Fatma Kılınç-Karzan
  • Alex L. Wang
    • Categories Global Optimization Theory, Quadratic Programming, Semi-definite Programming Tags , , , ,

    Quadratically constrained quadratic programs (QCQPs) are a fundamental class of optimization problems well-known to be NP-hard in general. In this paper we study sufficient conditions for a convex hull result that immediately implies that the standard semidefinite program (SDP) relaxation of a QCQP is tight. We begin by outlining a general framework for proving such … Read more

    A hybrid projection-proximal point algorithm for solving nonmonotone variational inequality problems

  • Lei Ming
  • He Yiran
    • Categories Complementarity and Variational Inequalities

    A hybrid projection-proximal point algorithm is proposed for variational inequality problems. Though the usual proximal point method and its variants require that the mapping involved be monotone, at least pseudomonotone, we assume only that the so-called Minty variational inequality has a solution, in order to ensure the global convergence. This assumption is less stringent than … Read more

    Autonomous traffic at intersections: an optimization-based analysis of possible time, energy, and CO2 savings

  • Do Duc Le
  • Maximilian Merkert
  • Stephan Sorgatz
  • Mirko Hahn
  • Sebastian Sager
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering, Network Optimization Tags , , , , , ,

    In the growing field of autonomous driving, traffic-light controlled intersections as the nodes of large traffic networks are of special interest. We want to analyze how much an optimized coordination of vehicles and infrastructure can contribute to a more efficient transit through these bottlenecks. In addition, we are interested in sensitivity of the results with … Read more

    Integer packing sets form a well-quasi-ordering

  • Alberto Del Pia
  • Dion C. Gijswijt
  • Jeff Linderoth
  • Haoran Zhu
    • Categories (Mixed) Integer Linear Programming

    An integer packing set is a set of non-negative integer vectors with the property that, if a vector x is in the set, then every non-negative integer vector y with y ≤ x is in the set as well. Integer packing sets appear naturally in Integer Optimization. In fact, the set of integer points in … Read more

    On the algebraic structure of the copositive cone

  • Roland Hildebrand
    • Categories Applications - OR and Management Sciences, Global Optimization Theory Tags , , ,

    We decompose the copositive cone $\copos{n}$ into a disjoint union of a finite number of open subsets $S_{\cal E}$ of algebraic sets $Z_{\cal E}$. Each set $S_{\cal E}$ consists of interiors of faces of $\copos{n}$. On each irreducible component of $Z_{\cal E}$ these faces generically have the same dimension. Each algebraic set $Z_{\cal E}$ is … Read more

    Compact Representations of Structured BFGS Matrices

  • Johannes Brust
  • Sven Leyffer
  • Zichao (Wendy) Di
  • Cosmin G. Petra
    • Categories Nonlinear Optimization Tags , , , ,

    For general large-scale optimization problems compact representations exist in which recursive quasi-Newton update formulas are represented as compact matrix factorizations. For problems in which the objective function contains additional structure, so-called structured quasi-Newton methods exploit available second-derivative information and approximate unavailable second derivatives. This article develops the compact representations of two structured Broyden-Fletcher-Goldfarb-Shanno update formulas. … Read more