Frank E. Curtis

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

    A Stochastic-Gradient-based Interior-Point Algorithm for Solving Smooth Bound-Constrained Optimization Problems

  • Qi Wang
  • Frank E. Curtis
  • Daniel P. Robinson
  • Vyacheslav Kungurtsev
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization in Data Science Tags , ,

    A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results. The algorithm is unique from other interior-point methods for solving smooth (nonconvex) optimization problems since the search directions are computed using stochastic gradient estimates. It is also unique … Read more

    Sequential Quadratic Optimization for Stochastic Optimization with Deterministic Nonlinear Inequality and Equality Constraints

  • Frank E. Curtis
  • Daniel P. Robinson
  • Baoyu Zhou
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Programming Tags , ,

    A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is tractable to evaluate constraint function and derivative values in each iteration, but it is intractable to evaluate the objective function or … Read more

    Worst-Case Complexity of TRACE with Inexact Subproblem Solutions for Nonconvex Smooth Optimization

  • Frank E. Curtis
  • Qi Wang
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

    An algorithm for solving nonconvex smooth optimization problems is proposed, analyzed, and tested. The algorithm is an extension of the Trust Region Algorithm with Contractions and Expansions (TRACE) [Math. Prog. 162(1):132, 2017]. In particular, the extension allows the algorithm to use inexact solutions of the arising subproblems, which is an important feature for solving large-scale … Read more

    Exploiting Prior Function Evaluations in Derivative-Free Optimization

  • Frank E. Curtis
  • Shima Dezfulian
  • Andreas Wächter
    • Categories Bound-constrained Optimization, Nonlinear Optimization Tags , ,

    A derivative-free optimization (DFO) algorithm is presented. The distinguishing feature of the algorithm is that it allows for the use of function values that have been made available through prior runs of a DFO algorithm for solving prior related optimization problems. Applications in which sequences of related optimization problems are solved such that the proposed … Read more

    Worst-Case Complexity of an SQP Method for Nonlinear Equality Constrained Stochastic Optimization

  • Frank E. Curtis
  • Michael O'Neill
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , ,

    A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear equality constraints. Barring additional terms that arise due to the adaptivity of the monotonically nonincreasing merit parameter sequence, the proved complexity bound is … Read more

    Inexact Sequential Quadratic Optimization for Minimizing a Stochastic Objective Function Subject to Deterministic Nonlinear Equality Constraints

  • Frank E. Curtis
  • Daniel P. Robinson
  • Baoyu Zhou
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , , ,

    An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is assumed that constraint function and derivative values can be computed, but that only stochastic approximations are available for the objective function and its … Read more

    A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear Equality Constrained Optimization with Rank-Deficient Jacobians

  • Albert S. Berahas
  • Frank E. Curtis
  • Michael O'Neill
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization, Statistics Tags , , , ,

    A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear equality constrained optimization problems in which the objective function is defined by an expectation of a stochastic function. The algorithmic structure of the proposed method is based on a step decomposition strategy that is known in the literature to be widely effective in practice, … Read more

    A Subspace Acceleration Method for Minimization Involving a Group Sparsity-Inducing Regularizer

  • Frank E. Curtis
  • Daniel P. Robinson
  • Yutong Dai
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags , , , , , , ,

    We consider the problem of minimizing an objective function that is the sum of a convex function and a group sparsity-inducing regularizer. Problems that integrate such regularizers arise in modern machine learning applications, often for the purpose of obtaining models that are easier to interpret and that have higher predictive accuracy. We present a new … Read more

    Sequential Quadratic Optimization for Nonlinear Equality Constrained Stochastic Optimization

  • Albert S. Berahas
  • Frank E. Curtis
  • Daniel P. Robinson
  • Baoyu Zhou
    • Categories Nonlinear Optimization Tags , ,

    Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic, and constraint function and derivative values can be computed explicitly, but the objective function is stochastic. It is assumed in this setting that it … Read more