Applications – Science and Engineering

Tutorials on Advanced Optimization Methods

  • Wei Wei
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering

    This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization technique and mixed-integer linear programming, robust optimization, and equilibrium/game problems. It discusses how to reformulate a difficult problem to a solver-compatible form via convexi cation, linearization, and decomposition, so the original problem can be reliably solved by … Read more

    Exact Penalty Function for L21 Norm Minimization over the Stiefel Manifold

  • Nachuan Xiao
  • Xin Liu
  • Ya-xiang Yuan
    • Categories Constrained Nonlinear Optimization, Statistics Tags , , ,

    L21 norm minimization with orthogonality constraints, feasible region of which is called Stiefel manifold, has wide applications in statistics and data science. The state-of-the-art approaches adopt proximal gradient technique on either Stiefel manifold or its tangent spaces. The consequent subproblem does not have closed-form solution and hence requires an iterative procedure to solve which is … Read more

    Benders decomposition for Network Design Covering Problems

  • Victor Bucarey
  • Bernard Fortz
  • Martine LabbĂ©
  • Juan A. Mesa
  • Natividad González-Blanco
    • Categories Facility Planning and Design, Transportation Tags , , ,

    We consider two covering variants of the network design problem. We are given a set of origin/destination(O/D) pairs and each such O/D pair is covered if there exists a path in the network from the origin to the destination whose length is not larger than a given threshold. In the first problem, called the maximal … 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

    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

    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

    Optimal design of an electricity-intensive industrial facility subject to electricity price uncertainty: stochastic optimization and scenario reduction

  • Adam R. Brandt
  • Holger Teichgraeber
    • Categories Chemical Engineering, Production and Logistics, Stochastic Programming Tags , , , ,

    When considering the design of electricity-intensive industrial processes, a challenge is that future electricity prices are highly uncertain. Design decisions made before construction can affect operations decades into the future. We thus explore whether including electricity price uncertainty into the design process affects design decisions. We apply stochastic optimization to the design and operations of … Read more

    KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

  • Drew P. Kouri
  • Denis Ridzal
  • Ray Tuminaro
    • Categories Control Applications, Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the … Read more

    Combination Chemotherapy Optimization

  • Temitayo Ajayi
  • Seyedmohammadhossein Hosseinian
  • Andrew J. Schaefer
  • Clifton D. Fuller
    • Categories (Mixed) Integer Linear Programming, Biomedical Applications Tags , ,

    Chemotherapy is one of the primary modalities of cancer treatment. Chemotherapy drug administration is a complex problem that often requires expensive clinical trials to evaluate potential regimens. One way to alleviate this burden and better inform future trials is to build reliable models for drug administration. Previous chemotherapy optimization models have mainly relied on optimal … Read more

    Mixed-Integer Optimal Control for Multimodal Chromatography

  • Hans Georg Bock
  • Christian Kirches
  • Andreas Potschka
  • Dominik H. Cebulla
    • Categories (Mixed) Integer Nonlinear Programming, Chemical Engineering, Systems governed by Differential Equations Optimization Tags , , ,

    Multimodal chromatography is a powerful tool in the downstream processing of biopharmaceuticals. To fully benefit from this technology, an efficient process strategy must be determined beforehand. To facilitate this task, we employ a recent mechanistic model for multimodal chromatography, which takes salt concentration and pH into account, and we present a mathematical framework for the … Read more