nonlinear optimization

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 J. 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

    Adaptive Regularization Minimization Algorithms with Non-Smooth Norms

  • Serge Gratton
  • Philippe L. Toint
    • Categories Unconstrained Optimization Tags , , , ,

    A regularization algorithm (AR1pGN) for unconstrained nonlinear minimization is considered, which uses a model consisting of a Taylor expansion of arbitrary degree and regularization term involving a possibly non smooth norm. It is shown that the non-smoothness of the norm does not affect the O(\epsilon_1^{-(p+1)/p}) upper bound on evaluation complexity for finding first-order \epsilon_1-approximate minimizers … Read more

    Solving Bang-Bang Problems Using The Immersed Interface Method and Integer Programming

  • Sarah Strikwerda
  • Ryan Vogt
    • Categories Combinatorial Optimization, Nonlinear Optimization Tags , , ,

    In this paper we study numerically solving optimal control problems with bang-bang control functions. We present a formal Lagrangian approach for solving the optimal control problem, and address difficulties encountered when numerically solving the state and adjoint equations by using the immersed interface method. We note that our numerical approach does not approximate the discontinuous … Read more

    Hölder Gradient Descent and Adaptive Regularization Methods in Banach Spaces for First-Order Points

  • Serge Gratton
  • Philippe L. Toint
  • Sadok Jerad
    • Categories Unconstrained Optimization Tags , ,

    This paper considers optimization of smooth nonconvex functionals in smooth infinite dimensional spaces. A Hölder gradient descent algorithm is first proposed for finding approximate first-order points of regularized polynomial functionals. This method is then applied to analyze the evaluation complexity of an adaptive regularization method which searches for approximate first-order points of functionals with $\beta$-H\”older … Read more

    Penetration depth between two convex polyhedra: An efficient global optimization approach

  • Mark A. Abramson
  • Griffin D. Kent
  • Gavin W. Smith
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Global Optimization Applications Tags , , , ,

    During the detailed design phase of an aerospace program, one of the most important consistency checks is to ensure that no two distinct objects occupy the same physical space. Since exact geometrical modeling is usually intractable, geometry models are discretized, which often introduces small interferences not present in the fully detailed model. In this paper, … Read more

    On the Numerical Performance of Derivative-Free Optimization Methods Based on Finite-Difference Approximations

  • Jorge Nocedal
  • Hao-Jun Shi
  • Melody Xuan
  • Figen Oztoprak
    • Categories Nonlinear Optimization Tags , , , ,

    The goal of this paper is to investigate an approach for derivative-free optimization that has not received sufficient attention in the literature and is yet one of the simplest to implement and parallelize. It consists of computing gradients of a smoothed approximation of the objective function (and constraints), and employing them within established codes. These … Read more

    TREGO: a Trust-Region Framework for Efficient Global Optimization

  • Youssef Diouane
  • V. Picheny
  • R. Le Riche
  • A. Scotto Di Perrotolo
    • Categories Global Optimization Tags , , ,

    Efficient Global Optimization (EGO) is the canonical form of Bayesian optimization that has been successfully applied to solve global optimization of expensive-to-evaluate black-box problems. However, EGO struggles to scale with dimension, and offers limited theoretical guarantees. In this work, a trust-region framework for EGO (TREGO) is proposed and analyzed. TREGO alternates between regular EGO steps … Read more

    On scaled stopping criteria for a safeguarded augmented Lagrangian method with theoretical guarantees

  • Roberto Andreani
  • Gabriel Haeser
  • Paulo J. S. Silva
  • María Laura Schuverdt
  • Leonardo D. Secchin
    • Categories Nonlinear Optimization Tags , , ,

    This paper discusses the use of a stopping criterion based on the scaling of the Karush-Kuhn-Tucker (KKT) conditions by the norm of the approximate Lagrange multiplier in the ALGENCAN implementation of a safeguarded augmented Lagrangian method. Such stopping criterion is already used in several nonlinear programming solvers, but it has not yet been considered in … 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