Basic Sciences Applications

A Survey of Recent Scalability Improvements for Semidefinite Programming with Applications in Machine Learning, Control, and Robotics

  • Amir Ali Ahmadi
  • Georgina Hall
  • Anirudha Majumdar
    • Categories Basic Sciences Applications, Control Applications, Semi-definite Programming Tags , , , ,

    Historically, scalability has been a major challenge to the successful application of semidefinite programming in fields such as machine learning, control, and robotics. In this paper, we survey recent approaches for addressing this challenge including (i) approaches for exploiting structure (e.g., sparsity and symmetry) in a problem, (ii) approaches that produce low-rank approximate solutions to … Read more

    Basis Pursuit Denoise with Nonsmooth Constraints

  • Aleksandr Y. Aravkin
  • Robert Baraldi
  • Rajiv Kumar
    • Categories Basic Sciences Applications, Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    Level-set optimization formulations with data-driven constraints minimize a regularization functional subject to matching observations to a given error level. These formulations are widely used, particularly for matrix completion and sparsity promotion in data interpolation and denoising. The misfit level is typically measured in the l2 norm, or other smooth metrics. In this paper, we present … Read more

    Time-Varying Semidefinite Programs

  • Amir Ali Ahmadi
  • Bachir El Khadir
    • Categories Basic Sciences Applications, Infinite Dimensional Optimization, Semi-definite Programming Tags , , , , ,

    We study time-varying semidefinite programs (TV-SDPs), which are semidefinite programs whose data (and solutions) are functions of time. Our focus is on the setting where the data varies polynomially with time. We show that under a strict feasibility assumption, restricting the solutions to also be polynomial functions of time does not change the optimal value … Read more

    Forecasting Solar Flares using magnetogram-based predictors and Machine Learning

  • Federico Benvenuto
  • Manolis K. Georgoulis
  • D. Shaun Bloomfield
  • Kostas Florios
  • Jordan A. Guerra
  • Ioannis Kontogiannis
  • Sung-Hong Park
    • Categories Basic Sciences Applications, Data-Mining, Statistics Tags ,

    We propose a forecasting approach for solar flares based on data from Solar Cycle 24, taken by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) mission. In particular, we use the Space-weather HMI Active Region Patches (SHARP) product that facilitates cut-out magnetograms of solar active regions (AR) in the Sun … Read more

    Optimization of Stochastic Problems with Probability Functions via Differential Evolution

  • Bayrammyrat Myradov
    • Categories Basic Sciences Applications, Stochastic Approaches, Stochastic Programming

    Chance constrained programming, quantile/Value-at-Risk (VaR) optimization and integral quantile / Conditional Value-at-Risk (CVaR) optimization problems as Stochastic Programming Problems with Probability Functions (SPP-PF) are one of the most widely studied optimization problems in recent years. As a rule real-life SPP-PF is nonsmooth nonconvex optimization problem with complex geometry of objective function. Moreover, often it cannot … Read more

    A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilation

  • Serge Gratton
  • Philippe L. Toint
  • Selime Gürol
  • Ehouarn Simon
    • Categories Basic Sciences Applications, Nonlinear Systems and Least-Squares Tags , ,

    The effect of preconditioning linear weighted least-squares using an approximation of the model matrix is analyzed, showing the interplay of the eigenstructures of both the model and weighting matrices. A small example is given illustrating the resulting potential inefficiency of such preconditioners. Consequences of these results in the context of the weakly-constrained 4D-Var data assimilation … Read more

    On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation

  • Serge Gratton
  • Philippe L. Toint
  • Selime Gürol
  • Ehouarn Simon
    • Categories Basic Sciences Applications, Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , , ,

    This paper discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationaly coherent variants of the algorithm … Read more

    Optimal threshold classification characteristics

  • David Kisets
    • Categories Basic Sciences Applications, Optimization of Simulated Systems Tags , , ,

    This study looks at the application of mathematical concepts of entropy and Fibonacci sequence in creating optimal dimensional relations of classification character. The paper is devoted to optimization of some numerical relations and integers as unified threshold characteristics of classification type, aimed for example at systemic optimizing the measuring information of various processes. The paper … Read more

    A MIQCP formulation for B-spline constraints

  • Bjarne Grimstad
    • Categories (Mixed) Integer Nonlinear Programming, Basic Sciences Applications Tags , , , ,

    This paper presents a mixed-integer quadratically constrained programming (MIQCP) formulation for B-spline constraints. The formulation can be used to obtain an exact MIQCP reformulation of any spline-constrained optimization problem, provided that the polynomial spline functions are continuous. This reformulation allows practitioners to use a general-purpose MIQCP solver, instead of a special-purpose spline solver, when solving … Read more

    Sequential Linear Programming and Particle Swarm Optimization for the optimization of energy districts

  • Stefania Bellavia
  • Elisa Riccietti
  • Stefano Sello
    • Categories Basic Sciences Applications, Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    In this paper we deal with the optimization of energy resources management of industrial districts, with the aim of minimizing the customer energy expenses. In a district the number of possible energy system combinations is really large, and a manual design approach might lead to a suboptimal solution. For this reason we designed a software … Read more