An optimal classifier for the generation of fair and calibrated synthetic data

  • Maria Eduarda Pinheiro
  • Jan Pablo Burgard
  • João Vitor Pamplona
    • Categories Applications - OR and Management Sciences Tags , , ,

      For agent based micro simulations, as used for example for epidemiological modeling during the COVID-19 pandemic, a realistic base population is crucial. Beyond demographic variables, health-related variables should also be included. In Germany, health-related surveys are typically small in scale, which presents several challenges when generating these variables. Specifically, strongly imbalanced classes and insufficient … Read more

    The L-Shaped Method for Stochastic Programs with Decision-Dependent Uncertainty

  • Giovanni Pantuso
    • Categories Stochastic Programming

    In this paper we extend the well-known L-Shaped method to solve two-stage stochastic programming problems with decision-dependent uncertainty. The method is based on a novel, unifying, formulation and on distribution-specific optimality and feasibility cuts for both linear and integer stochastic programs. Extensive tests on three production planning problems illustrate that the method is extremely effective … Read more

    Two approaches to piecewise affine approximation

  • nsukhorukova
    • Categories Applications - OR and Management Sciences, Approximation Algorithms, Data-Mining Tags , , ,

    The problem of approximation by piecewise affine functions has been studied for several decades (least squares and uniform approximation). If the location of switches from one affine piece to another (knots for univariate approximation) is known the problem is convex and there are several approaches to solve this problem. If the location of such switches … Read more

    Full Convergence of Regularized Methods for Unconstrained Optimization

  • Andrea Cristofari
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , ,

    Typically, the sequence of points generated by an optimization algorithm may have multiple limit points. Under convexity assumptions, however, (sub)gradient methods are known to generate a convergent sequence of points. In this paper, we extend the latter property to a broader class of algorithms. Specifically, we study unconstrained optimization methods that use local quadratic models … Read more

    Dual certificates of primal cone membership

  • Joonyeob Lee
  • Dávid Papp
  • Anita Varga
    • Categories Cone Programming, Convex Optimization, Semi-definite Programming Tags , , , , ,

    We discuss easily verifiable cone membership certificates, that is, certificates proving relations of the form \( b\in K \) for convex cones \(K\) that consist of vectors in the dual cone \(K^*\). Vectors in the dual cone are usually associated with separating hyperplanes, and so they are interpreted as certificates of non-membership in the standard … Read more

    Algorithmic Approaches for Identifying the Trade-off between Pessimism and Optimism in a Stochastic Fixed Charge Facility Location Problem

  • Man Yiu Tsang
  • Karmel S. Shehadeh
    • Categories Facility Planning and Design, Robust Optimization, Stochastic Programming Tags , , ,

    We introduce new algorithms to identify the trade-off (TRO) between adopting a distributional belief and hedging against ambiguity when modeling uncertainty in a capacitated fixed charge facility location problem (CFLP). We first formulate a TRO model for the CFLP (TRO-CFLP), which determines the number of facilities to open by minimizing the fixed establishment cost and … Read more

    Worst-Case Complexity of High-Order Algorithms for Pareto-Front Reconstruction

  • Andrea Cristofari
  • Marianna De Santis
  • Giampaolo Liuzzi
  • Stefano Lucidi
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags , ,

    In this paper, we are concerned with a worst-case complexity analysis of a-posteriori algorithms for unconstrained multiobjective optimization. Specifically, we propose an algorithmic framework that generates sets of points by means of $p$th-order models regularized with a power $p+1$ of the norm of the step. Through a tailored search procedure, several trial points are generated … Read more

    ASMOP: Additional sampling stochastic trust region method for multi-objective problems

  • Nataša Krklec Jerinkić
  • Luka Rutešić
    • Categories Multi-Criteria Optimization, Optimization of Systems modeled by PDEs, Stochastic Programming Tags , , , , ,

    We consider an unconstrained multi-criteria optimization problem with finite sum objective functions. The proposed algorithm belongs to a non-monotone trust-region framework where additional sampling approach is used to govern the sample size and the acceptance of a candidate point. Depending on the problem, the method can result in a mini-batch or an increasing sample size … Read more

    A Dantzig-Wolfe Single-Level Reformulation for Mixed-Integer Linear Bilevel Optimization: Exact and Heuristic Approaches

  • Henri Lefebvre
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, Bilevel Optimization, Branch and Cut Algorithms Tags , , , ,

    Bilevel optimization problems arise in numerous real-world applications. While single-level reformulations are a common strategy for solving convex bilevel problems, such approaches usually fail when the follower’s problem includes integer variables. In this paper, we present the first single-level reformulation for mixed-integer linear bilevel optimization, which does not rely on the follower’s value function. Our … Read more

    Relaxations of KKT Conditions do not Strengthen Finite RLT and SDP-RLT Bounds for Nonconvex Quadratic Programs

  • E. Alper Yildirim
    • Categories Global Optimization, Linear, Cone and Semidefinite Programming, Quadratic Programming Tags , , , ,

    We consider linear and semidefinite programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT relaxation), and the Shor relaxation combined with the RLT relaxation (SDP-RLT relaxation). By incorporating the first-order optimality conditions, a quadratic program can be formulated as an optimization problem with complementarity constraints. We investigate the effect of incorporating optimality … Read more