Month: July 2020

Strong Formulations for Distributionally Robust Chance-Constrained Programs with Left-Hand Side Uncertainty under Wasserstein Ambiguity

  • Nam Ho-Nguyen
  • Fatma Kılınç-Karzan
  • Simge Küçükyavuz
  • Dabeen Lee
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    Distributionally robust chance-constrained programs (DR-CCP) over Wasserstein ambiguity sets exhibit attractive out-of-sample performance and admit big-$M$-based mixed-integer programming (MIP) reformulations with conic constraints. However, the resulting formulations often suffer from scalability issues as sample size increases. To address this shortcoming, we derive stronger formulations that scale well with respect to the sample size. Our focus … Read more

    Characterization of an Anomalous Behavior of a Practical Smoothing Technique

  • Pedro Borges de Melo
    • Categories Game Theory, Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    A practical smoothing method was analyzed and tested against state-of-the-art solvers for some non-smooth optimization problems in [BSS20a; BSS20b]. This method can be used to smooth the value functions and solution mappings of fully parameterized convex problems under mild conditions. In general, the smoothing of the value function lies from above the true value function … Read more

    Priority Based Flow Improvement with Intermediate Storage

  • Mohan Chandra Adhikari
  • Urmila Pyakurel
    • Categories Network Optimization Tags , , ,

    Every models in the network flow theory aim to increase flow value from the sources to the sinks and reduce time or cost satisfying the capacity and flow conservation constraints. Recently, the network flow model without flow conservation constraints at the intermediate nodes has been investigated by Pyakurel and Dempe \cite{pyadem:2019}. In this model, if … Read more

    Mathematical Programming formulations for the Alternating Current Optimal Power Flow problem

  • Daniel Bienstock
  • Mauro Escobar
  • Claudio Gentile
  • Leo Liberti
    • Categories Energy, Global Optimization Applications, Quadratic Programming Tags , ,

    Power flow refers to the injection of power on the lines of an electrical grid, so that all the injections at the nodes form a consistent flow within the network. Optimality, in this setting, is usually intended as the minimization of the cost of generating power. Current can either be direct or alternating: while the … Read more

    The block mutual coherence property condition for signal recovery

  • Wang Hailin
  • Jianjun Wang
  • Jianwen Huang
  • Jia Jinping
  • Feng Zhang
    • Categories Data-Mining, Nonsmooth Optimization, Statistics

    Compressed sensing shows that a sparse signal can stably be recovered from incomplete linear measurements. But, in practical applications, some signals have additional structure, where the nonzero elements arise in some blocks. We call such signals as block-sparse signals. In this paper, the $\ell_2/\ell_1-\alpha\ell_2$ minimization method for the stable recovery of block-sparse signals is investigated. … Read more

    Improved optimization models for potential-driven network flow problems via ASTS orientations

  • Kai Helge Becker
  • Benjamin Hiller
    • Categories (Mixed) Integer Nonlinear Programming, Network Optimization Tags , , , ,

    The class of potential-driven network flow problems provides important models for a range of infrastructure networks that lead to hard-to-solve MINLPs in real-world applications. On large-scale meshed networks the relaxations usually employed are rather weak due to cycles in the network. To address this situation, we introduce the concept of ASTS orientations, a generalization of … Read more

    On a generalization of the Chvatal-Gomory closure

  • Sanjeeb Dash
  • Oktay Gunluk
  • Dabeen Lee
    • Categories Cutting Plane Approaches, Integer Programming Tags , , , , ,

    Many practical integer programming problems involve variables with one or two-sided bounds. Dunkel and Schulz (2012) considered a strengthened version of Chvatal-Gomory (CG) inequalities that use 0-1 bounds on variables, and showed that the set of points in a rational polytope that satisfy all these strengthened inequalities is a polytope. Recently, we generalized this result … Read more

    A Branch-and-Check Approach for the Tourist Trip Design Problem with Rich Constraints

  • Pierre Desport
  • Jorge E. Mendoza
  • Duc Minh Vu
  • Yannick Kergosien
    • Categories Branch and Cut Algorithms, Scheduling Tags , ,

    The tourist trip design problem is an extension of the orienteering problem applied to tourism. The problem consists in selecting a subset of locations to visit from among a larger set while maximizing the benefit for the tourist. The benefit is given by the sum of the rewards collected at each location visited. We consider … Read more

    Formulations and Valid Inequalities for Optimal Black Start Allocation in Power Systems

  • Ignacio Aravena
  • Shmuel Oren
  • Deepak Rajan
  • Georgios Patsakis
    • Categories (Mixed) Integer Linear Programming, Energy Tags , , ,

    The restoration of a power system after an extended blackout starts around units with enhanced technical capabilities, referred to as black start units (BSUs). We examine the planning problem of optimally allocating these units on the grid subject to a budget constraint. We present a mixed integer programming model based on current literature in power … Read more