A Line Search Multigrid Method for Large-Scale Convex Optimization

Abstract

We present a line search multigrid method based on Nash's MG/OPT multilevel optimization approach for solving discretized versions of convex infinite dimensional optimization problems. Global convergence is proved under fairly minimal requirements on the minimization method used at all grid levels. In particular, our convergence proof does not require that these minimization, or so-called (smoothing) steps, which we interpret in the context of optimization, be taken at each grid level in contrast with multigrid algorithms for PDEs, which fail to converge without such steps. Preliminary numerical experiments show that our method is promising.

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Document Details

Document Type
Technical Report
Publication Date
Jul 03, 2007
Accession Number
ADA478260

Entities

People

  • Donald Goldfarb
  • Zaiwen Wen

Organizations

  • Columbia University

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Boundaries
  • Computations
  • Computer Science
  • Convergence
  • Differential Equations
  • Equations
  • Grids
  • Image Processing
  • Industrial Engineering
  • Inequalities
  • Iterations
  • Notation
  • Operations Research
  • Optimization
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)