constrained equation

New Sufficient and Necessary Conditions for Constrained and Unconstrained Lipschitzian Error Bounds

  • Andreas Fischer
  • Alexey F. Izmailov
  • Mario Jelitte
    • Categories Complementarity and Variational Inequalities, Global Optimization Theory, Nonsmooth Optimization Tags , , , , , , ,

    Local error bounds play a fundamental role in mathematical programming and variational analysis. They are used e.g. as constraint qualifications in optimization, in developing calculus rules for generalized derivatives in nonsmooth and set-valued analysis, and they serve as a key ingredient in the design and convergence analysis of Newton-type methods for solving systems of possibly … Read more

    Convergence Conditions for Newton-type Methods Applied to Complementarity Systems with Nonisolated Solutions

  • Andreas Fischer
  • Alexey F. Izmailov
  • Markus Herrich
  • Mikhail V. Solodov
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization Tags , , , , , ,

    We consider a class of Newton-type methods for constrained systems of equations that involve complementarity conditions. In particular, at issue are the constrained Levenberg–Marquardt method and the recently introduced Linear Programming-Newton method, designed for the difficult case when solutions need not be isolated, and the equation mapping need not be differentiable at the solutions. We … Read more