Year: 2022

Statistical performance of subgradient step-size update rules in Lagrangian relaxations of chance-constrained optimization models

  • Charlotte Ritter
  • Bismark Singh
    • Categories Stochastic Programming Tags , , , ,

    Published in Lecture Notes in Computer Science. https://doi.org/10.1007/978-3-031-47859-8_26 Lagrangian relaxation schemes, coupled with a subgradient procedure, are frequently employed to solve chance-constrained optimization models. The subgradient procedure typically relies on a step-size update rule. Although there is extensive research on the properties of these step-size update rules, there is little consensus on which rules are … Read more

    A Successive Linear Relaxation Method for MINLPs with Multivariate Lipschitz Continuous Nonlinearities

  • Julia Grübel
  • Richard Krug
  • Martin Schmidt
  • Winnifried Wollner
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Global Optimization Tags , , , ,

    We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate them and that we know their global Lipschitz constants. The algorithm is a successive linear relaxation method in which we alternate … Read more

    A momentum-based linearized augmented Lagrangian method for nonconvex constrained stochastic optimization

  • Qiankun Shi
  • Xiao Wang
  • Hao Wang
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    Nonconvex constrained stochastic optimization has emerged in many important application areas. Subject to general functional constraints it minimizes the sum of an expectation function and a nonsmooth regularizer. Main challenges arise due to the stochasticity in the random integrand and the possibly nonconvex functional constraints. To address these issues we propose a momentum-based linearized augmented … Read more

    Two-stage distributionally robust noncooperative games: Existence of Nash equilibrium and its application to Cournot-Nash competition

  • Atsushi Hori
  • Nobuo Yamashita
    • Categories Game Theory Tags , , ,

    Two-stage distributionally robust stochastic noncooperative games with continuous decision variables are studied. In such games, each player solves a two-stage distributionally robust optimization problem depending on the decisions of the other players. Existing studies in this area have been limited with strict assumptions, such as linear decision rules, and supposed that each player solves a … Read more

    Worst-Case Analysis of Heuristic Approaches for the Temporal Bin Packing Problem with Fire-Ups

  • John Martinovic
  • Nico Strasdat
    • Categories (Mixed) Integer Linear Programming, Approximation Algorithms, Scheduling Tags , , , ,

    We consider the temporal bin packing problem with fire-ups (TBPP-FU), a branch of operations research recently introduced in multi-objective cloud computing. In this scenario, any item is equipped with a resource demand and a lifespan meaning that it requires the bin capacity only during that time interval. We then aim at finding a schedule minimizing … Read more

    Weighted Geometric Mean, Minimum Mediated Set, and Optimal Second-Order Cone Representation

  • Jie Wang
    • Categories Cone Programming, Convex Optimization, Second-Order Cone Programming Tags , , , ,

    We study optimal second-order cone representations for weighted geometric means, which turns out to be closely related to minimum mediated sets. Several lower bounds and upper bounds on the size of optimal second-order cone representations are proved. In the case of bivariate weighted geometric means (equivalently, one dimensional mediated sets), we are able to prove … Read more

    Superadditive duality and convex hulls for mixed-integer conic optimization

  • Akshay Gupte
  • Temitayo Ajayi
  • Amin Khademi
  • Andrew J. Schaefer
    • Categories (Mixed) Integer Nonlinear Programming, Cone Programming, Cutting Plane Approaches Tags , , ,

    We present an infinite family of linear valid inequalities for a mixed-integer conic program, and prove that these inequalities describe the convex hull of the feasible set when this set is bounded and described by integral data. The main element of our proof is to establish a new strong superadditive dual for mixed-integer conic programming … Read more

    Linear-size formulations for connected planar graph partitioning and political districting

  • Jack Zhang
  • Hamidreza Validi
  • Austin Buchanan
  • Illya V. Hicks
    • Categories Combinatorial Optimization, Integer Programming, Network Optimization

    Motivated by applications in political districting, we consider the task of partitioning the n vertices of a planar graph into k connected components. We propose an extended formulation that has two desirable properties: (i) it uses just O(n) variables, constraints, and nonzeros, and (ii) it is perfect. To explore its ability to solve real-world problems, … Read more

    An Efficient Pixel-based Packing Algorithm for Additive Manufacturing Production Planning

  • Hu Kanxin
    • Categories Meta Heuristics, Production and Logistics, Scheduling Tags , , ,

    Additive Manufacturing (AM), the technology of rapid prototyping directly from 3D digital models, has made a significant impact on both academia and industry. When facing the growing demand of AM services, AM production planning (AMPP) plays a vital role in reducing makespan and costs for AM service companies. This research focuses on the AMPP problem … Read more

    D-optimal Data Fusion: Exact and Approximation Algorithms

  • Yongchun Li
  • Marcia Fampa
  • Jon Lee
  • Feng Qiu
  • Weijun Xie
    • Categories Combinatorial Optimization, Integer Programming Tags , , , , , , ,

    We study the D-optimal Data Fusion (DDF) problem, which aims to select new data points, given an existing Fisher information matrix, so as to maximize the logarithm of the determinant of the overall Fisher information matrix. We show that the DDF problem is NP-hard and has no constant-factor polynomial-time approximation algorithm unless P = NP. … Read more