Vyacheslav Kungurtsev

Asynchronous Parallel Algorithms for Nonconvex Big-Data Optimization. Part II: Complexity and Numerical Results

  • Loris Cannelli
  • Francisco Facchinei
  • Vyacheslav Kungurtsev
  • Gesualdo Scutari
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Parallel Algorithms Tags , , ,

    We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex constraints. The proposed method hinges on successive convex approximation techniques and a novel probabilistic model that captures key elements of … Read more

    A predictor-corrector path-following algorithm for dual-degenerate parametric optimization problems

  • Johannes Jäschke
  • Vyacheslav Kungurtsev
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    Most path-following algorithms for tracing a solution path of a parametric nonlinear optimization problem are only certifiably convergent under strong regularity assumptions about the problem functions, in particular, the linear independence of the constraint gradients at the solutions, which implies a unique multiplier solution for every nonlinear program. In this paper we propose and prove … Read more

    A Globally Convergent Stabilized SQP Method: Superlinear Convergence

  • Philip E. Gill
  • Vyacheslav Kungurtsev
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization Tags , , , , , ,

    Regularized and stabilized sequential quadratic programming (SQP) methods are two classes of methods designed to resolve the numerical and theoretical difficulties associated with ill-posed or degenerate nonlinear optimization problems. Recently, a regularized SQP method has been proposed that allows convergence to points satisfying certain second-order KKT conditions (SIAM J. Optim., 23(4):1983–2010, 2013). The method is … Read more

    AN INEQUALITY-CONSTRAINED SQP METHOD FOR EIGENVALUE OPTIMIZATION

  • Moritz Diehl
  • Vyacheslav Kungurtsev
  • Wim Michiels
    • Categories Control Applications, Nonsmooth Optimization Tags , , , , , ,

    We consider a problem in eigenvalue optimization, in particular find- ing a local minimizer of the spectral abscissa – the value of a parameter that results in the smallest magnitude of the largest real part of the spectrum of a matrix system. This is an important problem for the stabilization of control sys- tems. Many … Read more

    SQP Methods for Parametric Nonlinear Optimization

  • Moritz Diehl
  • Vyacheslav Kungurtsev
    • Categories Nonlinear Optimization Tags , , , , , , ,

    Sequential quadratic programming (SQP) methods are known to be effi- cient for solving a series of related nonlinear optimization problems because of desirable hot and warm start properties–a solution for one problem is a good estimate of the solution of the next. However, standard SQP solvers contain elements to enforce global convergence that can interfere … Read more

    A Regularized SQP Method with Convergence to Second-Order Optimal Points

  • Philip E. Gill
  • Vyacheslav Kungurtsev
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , , ,

    Regularized and stabilized sequential quadratic programming methods are two classes of sequential quadratic programming (SQP) methods designed to resolve the numerical and theoretical difficulties associated with ill-posed or degenerate nonlinear optimization problems. Recently, a regularized SQP method has been proposed that provides a strong connection between augmented Lagrangian methods and stabilized SQP methods. The method … Read more