augmented Lagrangian function

Stochastic nested primal-dual method for nonconvex constrained composition optimization

  • Ling-Zi Jin
  • Xiao Wang
    • Categories Constrained Nonlinear Optimization, Data Science Algorithms, Stochastic Programming Tags , , , , , , ,

    \(\) In this paper we study the nonconvex constrained composition optimization, in which the objective contains a composition of two expected-value functions whose accurate information is normally expensive to calculate. We propose a STochastic nEsted Primal-dual (STEP) method for such problems. In each iteration, with an auxiliary variable introduced to track the inner layer function … Read more

    A momentum-based linearized augmented Lagrangian method for nonconvex constrained stochastic optimization

  • Qiankun Shi
  • Xiao Wang
  • Hao Wang
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    Nonconvex constrained stochastic optimization has emerged in many important application areas. Subject to general functional constraints it minimizes the sum of an expectation function and a nonsmooth regularizer. Main challenges arise due to the stochasticity in the random integrand and the possibly nonconvex functional constraints. To address these issues we propose a momentum-based linearized augmented … Read more