Applications – Science and Engineering

A Fully Distributed Dual Consensus ADMM Based on Partition for DC-OPF with Carbon Emission Trading

  • Zhaoyang Dong
  • Jiangyao Luo
  • Yan Xu
  • Linfeng Yang
  • Zhenrong Zhang
    • Categories Applications - Science and Engineering, Energy Tags , , , ,

    This paper presents a novel fully distributed alternating direction method of multipliers (ADMM) approach for solving the direct current optimal power flow with carbon emission trading (DC-OPF-CET) problem. Different from the other ADMM-based distributed approaches which disclosing boundary buses and branches information among adjacent subsystems, our proposed method adopts a new strategy by using ADMM … Read more

    Parallel and Distributed Successive Convex Approximation Methods for Big-Data Optimization

  • Gesualdo Scutari
  • Ying Sun
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , ,

    Recent years have witnessed a surge of interest in parallel and distributed optimization methods for large-scale systems. In particular, nonconvex large-scale optimization problems have found a wide range of applications in several engineering fields. The design and the analysis of such complex, large-scale, systems pose several challenges and call for the development of new optimization … Read more

    Provably High-Quality Solutions for the Meal Delivery Routing Problem

  • Martin Savelsbergh
  • Barış Yıldız
    • Categories Integer Programming, Optimization of Systems modeled by PDEs, Transportation Tags , , , , ,

    Online restaurant aggregators with integrated meal delivery networks have become more common and more popular in the past few years. Meal delivery is arguably the ultimate challenge in last mile logistics: a typical order is expected to be delivered within an hour (much less if possible), and within minutes of the food becoming ready. We … Read more

    The Synthesis Problem of Decentralized Energy Systems is strongly NP-hard

  • Martin Comis
  • Sebastian Goderbauer
  • Felix J. L. Willamowski
    • Categories Applications - Science and Engineering, Chemical Engineering, Combinatorial Optimization

    We analyze the computational complexity of the synthesis problem of decentralized energy systems. This synthesis problem consists of combining various types of energy conversion units and determining their sizing as well as operations in order to meet time-varying energy demands while maximizing an objective function, e.g., the net present value. In this paper, we prove … Read more

    Optimal switching sequence for switched linear systems

  • Qie He
  • Zeyang Wu
    • Categories Combinatorial Optimization, Control Applications, Dynamic Programming Tags , , , , ,

    We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of n-by-n matrices and an n-dimensional vector, find a sequence of K matrices, each chosen from the given set of matrices, to maximize a convex function over the product of the K matrices and the … Read more

    An Improved Flow-based Formulation and Reduction Principles for the Minimum Connectivity Inference Problem

  • Muhammad Abid Dar
  • Andreas Fischer
  • John Martinovic
  • Guntram Scheithauer
    • Categories Applications - Science and Engineering, Combinatorial Optimization, Integer Programming Tags , , ,

    The Minimum Connectivity Inference (MCI) problem represents an NP-hard generalisation of the well-known minimum spanning tree problem and has been studied in different fields of research independently. Let an undirected complete graph and finitely many subsets (clusters) of its vertex set be given. Then, the MCI problem is to find a minimal subset of edges … Read more

    The Cost of Not Knowing Enough: Mixed-Integer Optimization with Implicit Lipschitz Nonlinearities

  • Martin Schmidt
  • Mathias Sirvent
  • Winnifried Wollner
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Global Optimization Tags , , ,

    It is folklore knowledge that nonconvex mixed-integer nonlinear optimization problems can be notoriously hard to solve in practice. In this paper we go one step further and drop analytical properties that are usually taken for granted in mixed-integer nonlinear optimization. First, we only assume Lipschitz continuity of the nonlinear functions and additionally consider multivariate implicit … Read more

    Moments and convex optimization for analysis and control of nonlinear partial differential equations

  • Didier Henrion
  • Jean-Bernard Lasserre
  • Milan Korda
    • Categories Distributed Control, Optimization of Systems modeled by PDEs, Semi-definite Programming Tags , , , ,

    This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a \emph{linear} equation in the space of Borel measures. This equation is then used as a constraint of an infinite-dimensional linear programming problem (LP). This LP is … Read more

    Solving Pooling Problems by LP and SOCP Relaxations and Rescheduling Methods

  • Sunyoung Kim
  • Masaki Kimizuka
  • Makoto Yamashita
    • Categories Applications - Science and Engineering, Linear, Cone and Semidefinite Programming Tags , , , , ,

    The pooling problem is an important industrial problem in the class of network flow problems for allocating gas flow in pipeline transportation networks. For P-formulation of the pooling problem with time discretization, we propose second order cone programming (SOCP) and linear programming (LP) relaxations and prove that they obtain the same optimal value as the … Read more

    Derivative-Free Superiorization With Component-Wise Perturbations

  • Yair Censor
  • Howard Heaton
  • Reinhard W. Schulte
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , , ,

    Superiorization reduces, not necessarily minimizes, the value of a target function while seeking constraints-compatibility. This is done by taking a solely feasibility-seeking algorithm, analyzing its perturbations resilience, and proactively perturbing its iterates accordingly to steer them toward a feasible point with reduced value of the target function. When the perturbation steps are computationally efficient, this … Read more