Constrained Nonlinear Optimization

MadNCL: A GPU Implementation of Algorithm NCL for Large-Scale, Degenerate Nonlinear Programs

  • François Pacaud
  • Alexis Montoison
  • Dominique Orban
  • Sungho Shin
  • Michael A. Saunders
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization

    We present a GPU implementation of Algorithm NCL, an augmented Lagrangian method for solving large-scale and degenerate nonlinear programs. Although interior-point methods and sequential quadratic programming are widely used for solving nonlinear programs, the augmented Lagrangian method is known to offer superior robustness against constraint degeneracies and can rapidly detect infeasibility. We introduce several enhancements … Read more

    Progressively Sampled Equality-Constrained Optimization

  • Frank E. Curtis
  • Lingjun Guo
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization in Data Science Tags , , , ,

    An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the constraints are defined by an expectation or an average over a large (finite) number of terms. The main idea of the algorithm is to solve a sequence of equality-constrained problems, each involving a finite sample of constraint-function terms, over which … Read more

    On the Convergence and Properties of a Proximal-Gradient Method on Hadamard Manifolds

  • Glaydston Bento
  • Claudemir Rodrigues Santiago
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Nonsmooth Optimization Tags , , ,

    In this paper, we address composite optimization problems on Hadamard manifolds, where the objective function is given by the sum of a smooth term (not necessarily convex) and a convex term (not necessarily differentiable). To solve this problem, we develop a proximal gradient method defined directly on the manifold, employing a strategy that enforces monotonicity … Read more

    Active-Set Identification in Noisy and Stochastic Optimization

  • Lara Zebiane
  • Frank E. Curtis
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization in Data Science

    Identifying active constraints from a point near an optimal solution is important both theoretically and practically in constrained continuous optimization, as it can help identify optimal Lagrange multipliers and essentially reduces an inequality-constrained problem to an equality-constrained one. Traditional active-set identification guarantees have been proved under assumptions of smoothness and constraint qualifications, and assume exact … Read more

    On Relatively Smooth Optimization over Riemannian Manifolds

  • Chang He
  • Jiaxiang Li
  • Bo Jiang
  • Shiqian Ma
  • Shuzhong Zhang
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Programming Tags ,

    We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two Riemannian first-order methods, namely the retraction-based and projection-based Riemannian Bregman gradient methods, by incorporating the Bregman distance into the update steps. The retraction-based … Read more

    Primal-dual global convergence of an augmented Lagrangian method under the error bound condition

  • Roberto Andreani
  • Gabriel Haeser
  • Renan W. Prado
  • Leonardo D. Secchin
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    This work investigates global convergence properties of a safeguarded augmented Lagrangian method applied to nonlinear programming problems, with an emphasis on the role of constraint qualifications in ensuring boundedness of the Lagrange multiplier estimates, also known as dual sequences. When functions with locally Lipschitz continuous derivatives define the constraint set, we prove that the Error … Read more

    General Perturbation Resilient Dynamic String-Averaging for Inconsistent Problems with Superiorization

  • Kay Barshad
  • Yair Censor
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , , , , , , , , , , ,

    In this paper we introduce a General Dynamic String-Averaging (GDSA) iterative scheme and investigate its convergence properties in the inconsistent case, that is, when the input operators don’t have a common fixed point. The Dynamic String-Averaging Projection (DSAP) algorithm itself was introduced in an 2013 paper, where its strong convergence and bounded perturbation resilience were … Read more

    First-order methods for stochastic and finite-sum convex optimization with deterministic constraints

  • Zhaosong Lu
  • Yifeng Xiao
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Stochastic Programming Tags , , , , , ,

    In this paper, we study a class of stochastic and finite-sum convex optimization problems with deterministic constraints. Existing methods typically aim to find an \(\epsilon\)-expectedly feasible stochastic optimal solution, in which the expected constraint violation and expected optimality gap are both within a prescribed tolerance ϵ. However, in many practical applications, constraints must be nearly … Read more

    Efficient QUIC-Based Damped Inexact Iterative Reweighting for Sparse Inverse Covariance Estimation with Nonconvex Partly Smooth Regularization

  • Xiangyu Yang
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization, Semi-definite Programming Tags , , ,

    In this paper, we study sparse inverse covariance matrix estimation incorporating partly smooth nonconvex regularizers. To solve the resulting regularized log-determinant problem, we develop DIIR-QUIC—a novel Damped Inexact Iteratively Reweighted algorithm based on QUadratic approximate Inverse Covariance (QUIC) method. Our approach generalizes the classic iteratively reweighted \(\ell_1\) scheme through damped fixed-point updates. A key novelty … Read more

    Retrospective Approximation Sequential Quadratic Programming for Stochastic Optimization with General Deterministic Nonlinear Constraints

  • Shagun Gupta
  • Raghu Bollapragada
  • Albert S. Berahas
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization in Data Science Tags , , , ,

    In this paper, we propose a framework based on the Retrospective Approximation (RA) paradigm to solve optimization problems with a stochastic objective function and general nonlinear deterministic constraints. This framework sequentially constructs increasingly accurate approximations of the true problems which are solved to a specified accuracy via a deterministic solver, thereby decoupling the uncertainty from … Read more