Unbiased Subdata Selection for Fair Classification: A Unified Framework and Scalable Algorithms

  • Ye Qing
  • Weijun Xie
    • Categories (Mixed) Integer Nonlinear Programming, Data-Mining

    As an important problem in modern data analytics, classification has witnessed varieties of applications from different domains. Different from conventional classification approaches, fair classification concerns the issues of unintentional biases against the sensitive features (e.g., gender, race). Due to high nonconvexity of fairness measures, existing methods are often unable to model exact fairness, which can … Read more

    Some Modified Fast Iteration Shrinkage Thresholding Algorithms with a New Adaptive Non-monotone Stepsize Strategy for Nonsmooth and Convex Minimization Problems

  • Hongwei Liu
  • Wang Ting
  • Zexian Liu
    • Categories Convex and Nonsmooth Optimization Tags , , , , ,

    The ” fast iterative shrinkage-thresholding algorithm ” (FISTA) is one of the most famous first order optimization scheme, and the stepsize, which plays an important role in theoretical analysis and numerical experiment, is always determined by a constant related to the Lipschitz constant or by a backtracking strategy. In this paper, we design a new … Read more

    Planar Maximum Coverage Location Problem with Partial Coverage, Continuous Spatial Demand, and Adjustable Quality of Service

  • Manish Bansal
  • Parshin Shojaee
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization

    We consider a generalization of the classical planar maximum coverage location problem (PMCLP) in which partial coverage is allowed, facilities have adjustable quality of service (QoS) or service range, and demand zones and service zone of each facility are represented by two-dimensional spatial objects such as rectangles, circles, polygons, etc. We denote this generalization by … Read more

    Learning To Scale Mixed-Integer Programs

  • Timo Berthold
  • Gregor Hendel
    • Categories (Mixed) Integer Linear Programming, Linear Programming, Optimization Software Design Principles Tags , , , , , ,

    Many practical applications require the solution of numerically challenging linear programs (LPs) and mixed-integer programs (MIPs). Scaling is a widely used preconditioning technique that aims at reducing the error propagation of the involved linear systems, thereby improving the numerical behavior of the dual simplex algorithm and, consequently, LP-based branch-and-bound. A reliable scaling method often makes … Read more

    Stochastic RWA and Lightpath Rerouting in WDM Networks

  • Maryam Daryalal
  • Merve Bodur
    • Categories Stochastic Programming, Telecommunications Tags , , ,

    In a telecommunication network, Routing and Wavelength Assignment (RWA) is the problem of finding lightpaths for incoming connection requests. When facing a dynamic traffic, greedy assignment of lightpaths to incoming requests based on predefined deterministic policies leads to a fragmented network that cannot make use of its full capacity due to stranded bandwidth. At this … Read more

    A converging Benders’ decomposition algorithm for two-stage mixed-integer recourse models

  • Ward Romeijnders
  • Niels van der Laan
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , ,

    We propose a new solution method for two-stage mixed-integer recourse models. In contrast to existing approaches, we can handle general mixed-integer variables in both stages, and thus, e.g., do not require that the first-stage variables are binary. Our solution method is a Benders’ decomposition, in which we iteratively construct tighter approximations of the expected second-stage … Read more

    The Arc-Item-Load and Related Formulations for the Cumulative Vehicle Routing Problem

  • Mauro Henrique Mulati
  • Ricardo Fukasawa
  • Flávio Keidi Miyazawa
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization Tags , , , ,

    The Capacitated Vehicle Routing Problem (CVRP) consists of finding the cheapest way to serve a set of customers with a fleet of vehicles of a given capacity. While serving a particular customer, each vehicle picks up its demand and carries its weight throughout the rest of its route. While costs in the classical CVRP are … Read more

    ADMM and inexact ALM: the QP case

  • Stefano Cipolla
  • Jacek Gondzio
    • Categories Quadratic Programming Tags , ,

    Embedding randomization procedures in the Alternating Direction Method of Multipliers (ADMM) has recently attracted an increasing amount of interest as a remedy to the fact that the direct n-block generalization of ADMM is not necessarily convergent ($n \geq 3$). Even if, in practice, the introduction of such techniques could mitigate the diverging behaviour of the … Read more

    On complexity and convergence of high-order coordinate descent algorithms

  • V. S. Amaral
  • Roberto Andreani
  • Ernesto G. Birgin
  • José Mario Martínez
  • Diaulas S. Marcondes
    • Categories Nonlinear Optimization Tags , ,

    Coordinate descent methods with high-order regularized models for box-constrained minimization are introduced. High-order stationarity asymptotic convergence and first-order stationarity worst-case evaluation complexity bounds are established. The computer work that is necessary for obtaining first-order $\varepsilon$-stationarity with respect to the variables of each coordinate-descent block is $O(\varepsilon^{-(p+1)/p})$ whereas the computer work for getting first-order $\varepsilon$-stationarity with … Read more

    Twenty years of continuous multiobjective optimization in the twenty-first century

  • Gabriele Eichfelder
    • Categories Global Optimization, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    The survey highlights some of the research topics which have attracted attention in the last two decades within the area of mathematical optimization of multiple objective functions. We give insights into topics where a huge progress can be seen within the last years. We give short introductions to the specific sub-fields as well as some … Read more