Adaptive methods

An Adaptive and Parameter-Free Nesterov’s Accelerated Gradient Method for Convex Optimization

  • Jaewook J. Suh
  • Shiqian Ma
    • Categories Convex Optimization Tags , , , ,

    We propose AdaNAG, an adaptive accelerated gradient method based on Nesterov’s accelerated gradient method. AdaNAG is line-search-free, parameter-free, and achieves the accelerated convergence rates \( f(x_k) – f_\star = \mathcal{O}\left(1/k^2\right) \) and \( \min_{i\in\left\{1,\dots, k\right\}} \|\nabla f(x_i)\|^2 = \mathcal{O}\left(1/k^3\right) \) for \( L \)-smooth convex function \( f \). We provide a Lyapunov analysis for … Read more

    An adaptive superfast inexact proximal augmented Lagrangian method for smooth nonconvex composite optimization problems

  • Arnesh Sujanani
  • Renato D.C. Monteiro
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , , ,

    This work presents an adaptive superfast proximal augmented Lagrangian (AS-PAL) method for solving linearly-constrained smooth nonconvex composite optimization problems. Each iteration of AS-PAL inexactly solves a possibly nonconvex proximal augmented Lagrangian (AL) subproblem obtained by an aggressive/adaptive choice of prox stepsize with the aim of substantially improving its computational performance followed by a full Lagrangian … Read more

    Adaptive Nonlinear Optimization of District Heating Networks Based on Model and Discretization Catalogs

  • Hannes Dänschel
  • Volker Mehrmann
  • Marius Roland
  • Martin Schmidt
    • Categories Applications - Science and Engineering, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , ,

    We propose an adaptive optimization algorithm for operating district heating networks in a stationary regime. The behavior of hot water flow in the pipe network is modeled using the incompressible Euler equations and a suitably chosen energy equation. By applying different simplifications to these equations, we derive a catalog of models. Our algorithm is based … Read more