Constrained Nonlinear Optimization

Accelerating Stochastic Sequential Quadratic Programming for Equality Constrained Optimization using Predictive Variance Reduction

  • Albert S. Berahas
  • Jiahao Shi
  • Zihong Yi
  • Baoyu Zhou
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    In this paper, we propose a stochastic variance reduction method for solving equality constrained optimization problems. Specifically, we develop a method based on the sequential quadratic programming paradigm that utilizes gradient approximations via predictive variance reduction techniques. Under reasonable assumptions, we prove that a measure of first-order stationarity evaluated at the iterates generated by our … Read more

    A novel sequential optimality condition for smooth constrained optimization and algorithmic consequences

  • Renan W. Prado
  • Sandra A. Santos
  • Lucas E. A. Simões
    • Categories Constrained Nonlinear Optimization Tags , ,

    In the smooth constrained optimization setting, this work introduces the Domain Complementary Approximate Karush-Kuhn-Tucker (DCAKKT) condition, inspired by a sequential optimality condition recently devised for nonsmooth constrained optimization problems. It is shown that the augmented Lagrangian method can generate limit points satisfying DCAKKT, and it is proved that such a condition is not related to … Read more

    Improving the global convergence of Inexact Restoration methods for constrained optimization problems

  • Roberto Andreani
  • Alberto Ramos
  • Leonardo D. Secchin
    • Categories Constrained Nonlinear Optimization Tags , , ,

    Inexact restoration (IR) methods are an important family of numerical methods for solving constrained optimization problems with applications to electronic structures and bilevel programming among others areas. In these methods, the minimization is divided in two phases: decreasing infeasibility (feasibility phase) and improving optimality (optimality phase). The feasibility phase does not require the generated points … Read more

    Spectral Projected Subgradient Method for Nonsmooth Convex Optimization Problems

  • Nataša Krejić
  • Nataša Krklec Jerinkić
  • Tijana Ostojić
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Convex Optimization Tags , , , , ,

    We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy is employed. The proposed algorithm combines an SAA subgradient with the spectral coefficient in order to provide a suitable direction which improves … Read more

    Condensed interior-point methods: porting reduced-space approaches on GPU hardware

  • François Pacaud
  • Sungho Shin
  • Michel Schanen
  • Daniel A. Maldonado
  • Mihai Anitescu
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    The interior-point method (IPM) has become the workhorse method for nonlinear programming. The performance of IPM is directly related to the linear solver employed to factorize the Karush–Kuhn–Tucker (KKT) system at each iteration of the algorithm. When solving large-scale nonlinear problems, state-of-the art IPM solvers rely on efficient sparse linear solvers to solve the KKT … Read more

    Dissolving Constraints for Riemannian Optimization

  • Nachuan Xiao
  • Xin Liu
  • Kim-Chuan Toh
    • Categories Constrained Nonlinear Optimization, Unconstrained Optimization Tags , , ,

    In this paper, we consider optimization problems over closed embedded submanifolds of $\mathbb{R}^n$, which are defined by the constraints $c(x) = 0$. We propose a class of constraint dissolving approaches for these Riemannian optimization problems. In these proposed approaches, solving a Riemannian optimization problem is transferred into the unconstrained minimization of a constraint dissolving function … Read more

    New Penalized Stochastic Gradient Methods for Linearly Constrained Strongly Convex Optimization

  • Meng Li
  • Paul Grigas
  • Alper Atamturk
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , , ,

    For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective function terms. We provide upper bounds on the distance between the solutions to the original constrained problem and the penalty reformulations, … Read more

    Stable Recovery of Sparse Signals With Non-convex Weighted $r$-Norm Minus $1$-Norm

  • Jianwen Huang
  • Feng Zhang
  • Xinling Liu
  • Jianjun Wang
    • Categories Constrained Nonlinear Optimization, Data-Mining, Nonsmooth Optimization Tags , , ,

    Given the measurement matrix $A$ and the observation signal $y$, the central purpose of compressed sensing is to find the most sparse solution of the underdetermined linear system $y=Ax+z$, where $x$ is the $s$-sparse signal to be recovered and $z$ is the noise vector. Zhou and Yu \cite{Zhou and Yu 2019} recently proposed a novel … Read more

    Inexact Restoration for Minimization with Inexact Evaluation both of the Objective Function and the Constraints

  • Luís Felipe Bueno
  • F. Larreal
  • José Mario Martínez
    • Categories Constrained Nonlinear Optimization Tags , ,

    In a recent paper an Inexact Restoration method for solving continuous constrained optimization problems was analyzed from the point of view of worst-case functional complexity and convergence. On the other hand, the Inexact Restoration methodology was employed, in a different research, to handle minimization problems with inexact evaluation and simple constraints. These two methodologies are … Read more