Switching cost aware rounding for relaxations of mixed-integer optimal control problems: the two-dimensional case

  • Felix Bestehorn
  • Christoph Hansknecht
  • Christian Kirches
  • Paul Manns
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications Tags ,

    This article is concerned with a recently proposed switching cost aware rounding (SCARP) strategy in the combinatorial integral decomposition for mixed-integer optimal control problems (MIOCPs). We consider the case of a control variable that is discrete-valued and distributed on a two-dimensional domain. While the theoretical results from the one-dimensional case directly apply to the multidimensional … Read more

    A Planner-Trader Decomposition for Multi-Market Hydro Scheduling

  • Daniel Kuhn
  • Napat Rujeerapaiboon
  • Kilian Schindler
  • Wolfram Wiesemann
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming

    Peak/off-peak spreads on European electricity forward and spot markets are eroding due to the ongoing nuclear phaseout in Germany and the steady growth in photovoltaic capacity. The reduced profitability of peak/off-peak arbitrage forces hydropower producers to recover part of their original profitability on the reserve markets. We propose a bi-layer stochastic programming framework for the … Read more

    Controllable Transmission Networks UnderDemand Uncertainty with Modular FACTS

  • Alireza Soroudi
    • Categories Constrained Nonlinear Optimization, Optimization Software and Modeling Systems, Scheduling Tags , ,

    The transmission system operators (TSOs) are responsible to provide secure and efficient access to the transmission system for all stakeholders. This task is gradually getting challenging due to the demand growth, demand uncertainty, rapid changes in generation mix, and market policies. Traditionally, the TSOs try to maximize the technical performance of the transmission network via … Read more

    Infeasibility detection with primal-dual hybrid gradient for large-scale linear programming

  • David Applegate
  • Mateo Díaz
  • Haihao Lu
  • Miles Lubin
    • Categories Convex Optimization, Linear Programming Tags , , ,

    We study the problem of detecting infeasibility of large-scale linear programming problems using the primal-dual hybrid gradient method (PDHG) of Chambolle and Pock (2011). The literature on PDHG has mostly focused on settings where the problem at hand is assumed to be feasible. When the problem is not feasible, the iterates of the algorithm do … Read more

    A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimization

  • Nicolas Gillis
  • Le Thi Khanh Hien
  • Duy Nhat Phan
    • Categories Constrained Nonlinear Optimization Tags , , ,

    In this paper, we propose an algorithmic framework dubbed inertial alternating direction methods of multipliers (iADMM), for solving a class of nonconvex nonsmooth multiblock composite optimization problems with linear constraints. Our framework employs the general minimization-majorization (MM) principle to update each block of variables so as to not only unify the convergence analysis of previous … Read more

    Sparse Approximations with Interior Point Methods

  • Valentina De Simone
  • Daniela di Serafino
  • Jacek Gondzio
  • Spyridon Pougkakiotis
  • Marco Viola
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , , , ,

    Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well conditioned problems. In this paper, specialized variants of an interior point-proximal method of multipliers are proposed and analyzed for problems of this class. Computational experience … Read more

    An Approximation Algorithm for Indefinite Mixed Integer Quadratic Programming

  • Alberto Del Pia
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory

    In this paper we give an algorithm that finds an epsilon-approximate solution to a mixed integer quadratic programming (MIQP) problem. The algorithm runs in polynomial time if the rank of the quadratic function and the number of integer variables are fixed. The running time of the algorithm is expected unless P=NP. In order to design … Read more

    A General Framework for Optimal Control of Fractional Nonlinear Delay Systems by Wavelets

  • Malmir Iman
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , ,

    An iterative procedure to find the optimal solutions of general fractional nonlinear delay systems with quadraticperformance indices is introduced. The derivatives of state equations are understood in the Caputo sense. By presenting and applying a general framework, we use the Chebyshev wavelet method developed for fractional linear optimal control to convert fractional nonlinear optimal control … Read more

    Path Planning and Network Optimization for UAV Swarms for Multi-Target Tracking

  • Shawon Dey
  • Hans D Mittelmann
  • Shankarachary Ragi
    • Categories Applications - Science and Engineering

    This paper focuses on the development of decentralized collaborative sensing and sensor resource allocation algorithms where the sensors are located on-board autonomous unmanned aerial vehicles. We develop these algorithms in the context of single-target and multi-target tracking applications, where the objective is to maximize the tracking performance as measured by the mean-squared error between the … Read more

    A Comparative Study of Stability Representations for Solving Many-to-One Matching Problems with Utility-Weighted Objectives, Ties, and Incomplete Lists via Integer Optimization

  • Pitchaya Wiratchotisatian
  • Andrew C. Trapp
  • Hoda Atef Yekta
    • Categories Applications - OR and Management Sciences Tags , , , ,

    We consider integer optimization models for finding stable solutions to many-to-one, utility-weighted matching problems with incomplete preference lists and ties. While traditional algorithmic approaches for the stable many-to-one matching problem, such as the Deferred Acceptance algorithm, offer efficient performance for the strict problem setting, adaptation to alternative settings often requires careful customization. Optimization-based approaches are … Read more