Month: July 2020

An Adaptive Patch Approximation Algorithm for Bicriteria Convex Mixed Integer problems

  • Erik Diessel
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , , ,

    Pareto frontiers of bicriteria continuous convex problems can be efficiently computed and optimal theoretical performance bounds have been established. In the case of bicriteria mixed-integer problems, the approximation of the Pareto frontier becomes, however, significantly harder. In this paper, we propose a new algorithm for approximating the Pareto frontier of bicriteria mixed-integer programs with convex … Read more

    On Refinement Strategies for Solving MINLPs by Piecewise Linear Relaxations: A Generalized Red Refinement

  • Robert Burlacu
    • Categories (Mixed) Integer Nonlinear Programming Tags , , ,

    We investigate the generalized red refinement for n-dimensional simplices that dates back to Freudenthal in a mixed-integer nonlinear program (MINLP) context. We show that the red refinement meets sufficient convergence conditions for a known MINLP solution framework that is essentially based on solving piecewise linear relaxations. In addition, we prove that applying this refinement procedure … Read more

    An Almost Exact Solution to the Min Completion Time Variance in a Single Machine

  • Stefano Nasini
  • Rabia Nessah
    • Categories 0-1 Programming, Combinatorial Optimization, Scheduling Tags , , ,

    We consider a single machine scheduling problem to minimize the completion time variance of n jobs. This problem is known to be NP-hard and our contribution is to establish a novel bounding condition for a characterization of an optimal sequence. Specifically, we prove a necessary and sufficient condition (which can be verified in O(n\log n)) … Read more

    Power to Air-transportation via Hydrogen

  • Soheil Jafari
  • Alireza Soroudi
    • Categories Airline Optimization, Energy, Multidisciplinary Design Optimization Tags , , ,

    This paper proposes a framework to analyze the concept of power to hydrogen (P2H) for fueling the next generation of aircraft. The impact of introducing new P2H loads is investigated from different aspects namely, cost, carbon emission, and wind curtailment. The newly introduced electric load is calculated based on the idea of replacing the busiest … Read more

    Data-driven sample average approximation with covariate information

  • Rohit Kannan
  • Güzin Bayraksan
  • James R. Luedtke
    • Categories Stochastic Programming Tags , , , , ,

    We study optimization for data-driven decision-making when we have observations of the uncertain parameters within the optimization model together with concurrent observations of covariates. Given a new covariate observation, the goal is to choose a decision that minimizes the expected cost conditioned on this observation. We investigate three data-driven frameworks that integrate a machine learning … Read more

    LQR Design under Stability Constraints

  • Aleksandr Y. Aravkin
  • Anna Scampicchio
  • Gianluigi Pillonetto
    • Categories Control Applications

    The solution of classic discrete-time, finite-horizon linear quadratic regulator (LQR) problem is well known in literature. By casting the solution to be a static state-feedback, we propose a new method that trades off low LQR objective value with closed-loop stability. CitationTo appear on the special issue on the 21st IFAC World Congress 2020, IFAC PapersOnLine.ArticleDownload … Read more

    On the best achievable quality of limit points of augmented Lagrangian schemes

  • Roberto Andreani
  • Gabriel Haeser
  • Alberto Ramos
  • Leonardo M. Mito
  • Leonardo D. Secchin
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , ,

    The optimization literature is vast in papers dealing with improvements on the global convergence of augmented Lagrangian schemes. Usually, the results are based on weak constraint qualifications, or, more recently, on sequential optimality conditions obtained via penalization techniques. In this paper we propose a somewhat different approach, in the sense that the algorithm itself is … Read more

    Stochastic Zeroth-order Riemannian Derivative Estimation and Optimization

  • Krishnakumar Balasubramanian
  • Shiqian Ma
  • Jiaxiang Li
    • Categories Nonlinear Optimization

    We consider stochastic zeroth-order optimization over Riemannian submanifolds embedded in Euclidean space, where the task is to solve Riemannian optimization problem with only noisy objective function evaluations. Towards this, our main contribution is to propose estimators of the Riemannian gradient and Hessian from noisy objective function evaluations, based on a Riemannian version of the Gaussian … Read more

    A Manifold Proximal Linear Method for Sparse Spectral Clustering with Application to Single-Cell RNA Sequencing Data Analysis

  • Shixiang Chen
  • Shiqian Ma
  • Bingyuan Liu
  • Zhongruo Wang
  • Lingzhou Xue
  • Hongyu Zhao
    • Categories Nonlinear Optimization

    Spectral clustering is one of the fundamental unsupervised learning methods widely used in data analysis. Sparse spectral clustering (SSC) imposes sparsity to the spectral clustering and it improves the interpretability of the model. This paper considers a widely adopted model for SSC, which can be formulated as an optimization problem over the Stiefel manifold with … Read more

    Manifold Proximal Point Algorithms for Dual Principal Component Pursuit and Orthogonal Dictionary Learning

  • Shixiang Chen
  • Shiqian Ma
  • Anthony Man-Cho So
  • Zengde Deng
    • Categories Nonlinear Optimization

    We consider the problem of maximizing the $\ell_1$ norm of a linear map over the sphere, which arises in various machine learning applications such as orthogonal dictionary learning (ODL) and robust subspace recovery (RSR). The problem is numerically challenging due to its nonsmooth objective and nonconvex constraint, and its algorithmic aspects have not been well … Read more