Applications – Science and Engineering

Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints

  • Coralia Cartis
  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Data-Mining, Nonlinear Systems and Least-Squares Tags , , , , ,

    We provide sharp worst-case evaluation complexity bounds for nonconvex minimization problems with general inexpensive constraints, i.e.\ problems where the cost of evaluating/enforcing of the (possibly nonconvex or even disconnected) constraints, if any, is negligible compared to that of evaluating the objective function. These bounds unify, extend or improve all known upper and lower complexity bounds … Read more

    n-step cutset inequalities: facets for multi-module capacitated network design problem

  • Kiavash Kianfar
  • Haochen Luo
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches, Facility Planning and Design

    Many real-world decision-making problems can be modeled as network design problems, especially on networks with capacity requirements on links. In network design problems, decisions are made on installation of flow transfer capacities on the links and routing of flow from a set of source nodes to a set of sink nodes through the links. Many … Read more

    Towards Resilient Operation of Multi-Microgrids: An MISOCP-Based Frequency-Constrained Approach

  • Amin Gholami
  • Xu Andy Sun
    • Categories Applications - Science and Engineering, Control Applications, Energy Tags , , , , ,

    High penetration of distributed energy resources (DERs) is transforming the paradigm in power system operation. The ability to provide electricity to customers while the main grid is disrupted has introduced the concept of microgrids with many challenges and opportunities. Emergency control of dangerous transients caused by the transition between the grid-connected and island modes in … Read more

    Data-Driven Maintenance and Operations Scheduling in Power Systems under Decision-Dependent Uncertainty

  • Shabbir Ahmed
  • Nagi Gebraeel
  • Beste Basciftci
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering Tags , , ,

    Generator maintenance scheduling plays a pivotal role in ensuring uncompromising operations of power systems. There exists a tight coupling between the condition of the generators and corresponding operational schedules, significantly affecting reliability of the system. In this study, we effectively model and solve an integrated condition-based maintenance and operations scheduling problem for a fleet of … Read more

    On tradeoffs between treatment time and plan quality of volumetric-modulated arc therapy with sliding-window delivery

  • Lovisa Engberg
  • Anders Forsgren
    • Categories Applications - Science and Engineering Tags , , ,

    The purpose of this study is to give an exact formulation of optimization of volumetric-modulated arc therapy (VMAT) with sliding-window delivery, and to investigate the plan quality effects of decreasing the number of sliding-window sweeps made on the 360-degree arc for a faster VMAT treatment. In light of the exact formulation, we interpret an algorithm … Read more

    Global Convergence in Deep Learning with Variable Splitting via the Kurdyka-{\L}ojasiewicz Property

  • T Lau
  • S Lin
  • S Ouyang
  • Y Yuan
  • Jinshan Zeng
    • Categories Convex and Nonsmooth Optimization, Data-Mining Tags , , ,

    Deep learning has recently attracted a significant amount of attention due to its great empirical success. However, the effectiveness in training deep neural networks (DNNs) remains a mystery in the associated nonconvex optimizations. In this paper, we aim to provide some theoretical understanding on such optimization problems. In particular, the Kurdyka-{\L}ojasiewicz (KL) property is established … Read more

    Condition Number Analysis of Logistic Regression, and its Implications for Standard First-Order Solution Methods

  • Robert M. Freund
  • Rahul Mazumder
  • Paul Grigas
    • Categories Convex Optimization, Data-Mining, Statistics Tags , , ,

    Logistic regression is one of the most popular methods in binary classification, wherein estimation of model parameters is carried out by solving the maximum likelihood (ML) optimization problem, and the ML estimator is defined to be the optimal solution of this problem. It is well known that the ML estimator exists when the data is … Read more

    Resilient layout, design and operation of energy-efficient water distribution networks for high-rise buildings using MINLP

  • Lena C. Altherr
  • Marc E. Pfetsch
  • Andreas Schmitt
  • Philipp Leise
    • Categories (Mixed) Integer Nonlinear Programming, Mechanical Engineering, Robust Optimization Tags , , , , , , ,

    Water supply of high-rise buildings requires pump systems to ensure pressure requirements. The design goal of these systems are energy and cost efficiency, both in terms of fixed cost as well as during operation. In this paper, cost optimal decentralized and tree-shaped water distribution networks are computed, where placements of pumps at different locations in … Read more

    Learning a Mixture of Gaussians via Mixed Integer Optimization

  • Hari Bandi
  • Dimitris Bertsimas
  • Rahul Mazumder
    • Categories 0-1 Programming, Applications - OR and Management Sciences, Statistics Tags ,

    We consider the problem of estimating the parameters of a multivariate Gaussian mixture model (GMM) given access to $n$ samples $\x_1,\x_2,\ldots ,\x_n \in\mathbb{R}^d$ that are believed to have come from a mixture of multiple subpopulations. State-of-the-art algorithms used to recover these parameters use heuristics to either maximize the log-likelihood of the sample or try to … Read more

    Assessing the Cost of the Hazard-Decision Simplification in Multistage Stochastic Hydrothermal Scheduling

  • Andre Lawson
  • Alexandre Street
  • Davi Valladão
  • Alexandre Velloso
    • Categories Control Applications, Dynamic Programming, Stochastic Programming Tags , , ,

    Hydropower is one of the world’s primary renewable energy sources whose usage has profound economic, environmental, and social impacts. We focus on the dispatch of generating units and the storage policy of hydro resources. In this context, an accurate assessment of the water opportunity-cost is cru- cial for driving the sustainable use of this scarce … Read more