Applications – Science and Engineering

A Comparison of Nonsmooth, Nonconvex, Constrained Optimization Solvers for the Design of Time-Delay Compensators

  • Vyacheslav Kungurtsev
  • Tim Mitchell
  • Tomas Vyhlidal
    • Categories Control Applications, Nonsmooth Optimization, Optimization Software Benchmark

    We present a detailed set of performance comparisons of two state-of-the-art solvers for the application of designing time-delay compensators, an important problem in the field of robust control. Formulating such robust control mechanics as constrained optimization problems often involves objective and constraint functions that are both nonconvex and nonsmooth, both of which present significant challenges … Read more

    A note on solving nonlinear optimization problems in variable precision

  • Serge Gratton
  • Philippe L. Toint
    • Categories Applications - Science and Engineering, Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags ,

    This short note considers an efficient variant of the trust-region algorithm with dynamic accuracy proposed Carter (1993) and Conn, Gould and Toint (2000) as a tool for very high-performance computing, an area where it is critical to allow multi-precision computations for keeping the energy dissipation under control. Numerical experiments are presented indicating that the use … Read more

    Group sparse recovery in impulsive noise via alternating direction method of multipliers

  • Jianjun Wang
  • Jianwen Huang
  • Wang Wendong
  • Feng Zhang
    • Categories Applications - Science and Engineering, Control Applications, Data-Mining

    In this paper, we consider the recovery of group sparse signals corrupted by impulsive noise. In some recent literature, researchers have utilized stable data fitting models, like $l_1$-norm, Huber penalty function and Lorentzian-norm, to substitute the $l_2$-norm data fidelity model to obtain more robust performance. In this paper, a stable model is developed, which exploits … Read more

    Energy and Reserve Dispatch with Distributionally Robust Joint Chance Constraints

  • Daniel Kuhn
  • Viet Anh Nguyen
  • Christos Ordoudis
  • Pierre Pinson
    • Categories Applications - Science and Engineering, Robust Optimization, Stochastic Programming Tags , , ,

    We develop a two-stage stochastic program for energy and reserve dispatch, which ensures the safe operation of a power system with a high penetration of renewables and a strong interdependence with the natural gas system. Distributionally robust joint chance constraints with Wasserstein ambiguity sets ensure that there is no need for load shedding and renewable … 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

    Feature selection in SVM via polyhedral k-norm

  • Manlio Gaudioso
  • Enrico Gorgone
  • Jean-Baptiste Hiriart-Urruty
    • Categories Data-Mining, Global Optimization Tags , , , ,

    We treat the Feature Selection problem in the Support Vector Machine (SVM) framework by adopting an optimization model based on use of the $\ell_0$ pseudo–norm. The objective is to control the number of non-zero components of normal vector to the separating hyperplane, while maintaining satisfactory classification accuracy. In our model the polyhedral norm $\|.\|_{[k]}$, intermediate … Read more

    Adaptive regularization algorithms with inexact evaluations for nonconvex optimization

  • Stefania Bellavia
  • Benedetta Morini
  • Philippe L. Toint
  • Gianmarco Gurioli
    • Categories Constrained Nonlinear Optimization, Data-Mining, Unconstrained Optimization Tags , , , ,

    A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that is constraints whose evaluation and enforcement has negligible cost) under the assumption that the derivative of highest degree is beta-H\”{o}lder continuous. It features a … Read more

    A Unified Framework for Sparse Relaxed Regularized Regression: SR3

  • Aleksandr Y. Aravkin
  • Peng Zheng
  • Travis Askham
  • Steve Brunton
  • Nathan Kutz
    • Categories Nonlinear Systems and Least-Squares, Nonsmooth Optimization, Statistics Tags , , , ,

    Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications, vari- able selection, and high-dimensional analysis. We propose a broad framework for sparse relaxed regularized regression, called SR3. The key idea is to solve a relaxation of … Read more

    Strong mixed-integer programming formulations for trained neural networks

  • Ross Anderson
  • Joey Huchette
  • Juan Pablo Vielma
  • Will Ma
  • Christian Tjandraatmadja
    • Categories (Mixed) Integer Linear Programming, Statistics Tags , ,

    We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying that an image classification network is robust to adversarial inputs, or solving decision problems where the objective function is a machine learning model. … Read more

    Nonmonotonicity and Quasiconvexity on Equilibrium Problems

  • Lennin Mallma Ramirez
    • Categories Applications - Science and Engineering, Complementarity and Variational Inequalities, Nonsmooth Optimization

    In this note, some results are introduced considering the assumptions of quasiconvexity and nonmonotonicity, finally an application and an idea to solve the quasiconvex equilibrium problem are presented considering these new results. Article Download View Nonmonotonicity and Quasiconvexity on Equilibrium Problems