almost-sure convergence

AS-BOX: Additional Sampling Method for Weighted Sum Problems with Box Constraints

  • Nataša Krejić
  • Nataša Krklec Jerinkić
  • Tijana Ostojić
  • Nemanja Vučićević
    • Categories Bound-constrained Optimization, Nonlinear Optimization Tags , , , , ,

    A class of optimization problems characterized by a weighted finite-sum objective function subject to box constraints is considered. We propose a novel stochastic optimization method, named AS-BOX (Additional Sampling for BOX constraints), that combines projected gradient directions with adaptive variable sample size strategies and nonmonotone line search. The method dynamically adjusts the batch size based … Read more

    ASPEN: An Additional Sampling Penalty Method for Finite-Sum Optimization Problems with Nonlinear Equality Constraints

  • Nataša Krejić
  • Nataša Krklec Jerinkić
  • Tijana Ostojić
  • Nemanja Vučićević
    • Categories Nonlinear Optimization, Stochastic Approaches, Stochastic Programming Tags , , , , , ,

    We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework of quadratic penalty methods. Thus, depending on the problem at hand, the resulting method may exhibit a sample size strategy ranging from a mini-batch on one … Read more

    SMOP: Stochastic trust region method for multi-objective problems

  • Nataša Krejić
  • Nataša Krklec Jerinkić
  • Luka Rutešić
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    The problem considered is a multi-objective optimization problem, in which the goal is to find an optimal value of a vector function representing various criteria. The aim of this work is to develop an algorithm which utilizes the trust region framework with probabilistic model functions, able to cope with noisy problems, using inaccurate functions and … Read more

    Almost-sure convergence of iterates and multipliers in stochastic sequential quadratic optimization

  • Frank E. Curtis
  • Xin Jiang
  • Qi Wang
    • Categories Constrained Nonlinear Optimization, Data Science Applications, Stochastic Programming Tags , , ,

    Stochastic sequential quadratic optimization (SQP) methods for solving continuous optimization problems with nonlinear equality constraints have attracted attention recently, such as for solving large-scale data-fitting problems subject to nonconvex constraints. However, for a recently proposed subclass of such methods that is built on the popular stochastic-gradient methodology from the unconstrained setting, convergence guarantees have been … Read more

    LSOS: Line-search Second-Order Stochastic optimization methods for nonconvex finite sums

  • Daniela di Serafino
  • Nataša Krejić
  • Nataša Krklec Jerinkić
  • Marco Viola
    • Categories Nonlinear Optimization, Stochastic Programming Tags , , , ,

    We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients. The methods fitting into this framework combine line searches and suitably decaying step lengths. A key issue is a two-step sampling at … Read more