Constrained Nonlinear Optimization

A primal-dual modified log-barrier method for inequality constrained nonlinear optimization

  • Joshua D. Griffin
  • Riadh Omheni
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    We present a primal-dual modified log-barrier algorithm to solve inequality constrained nonlinear optimization problems. Basically, the algorithm is a Newton-like method applied to a perturbation of the optimality system that follows from a reformulation of the initial problem by introducing a modified log-barrier function to handle inequality constraints. The algorithm uses an outer/inner iteration scheme … Read more

    Nonconvex Constrained Optimization by a Filtering Branch and Bound

  • Gabriele Eichfelder
  • Kathrin Klamroth
  • Julia Niebling
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Multi-Criteria Optimization

    A major difficulty in optimization with nonconvex constraints is to find feasible solutions. As simple examples show, the alphaBB-algorithm for single-objective optimization may fail to compute feasible solutions even though this algorithm is a popular method in global optimization. In this work, we introduce a filtering approach motivated by a multiobjective reformulation of the constrained … Read more

    Active Set Complexity of the Away-step Frank-Wolfe Algorithm

  • Immanuel M. Bomze
  • Francesco Rinaldi
  • Damiano Zeffiro
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , ,

    In this paper, we study active set identification results for the away-step Frank-Wolfe algorithm in different settings. We first prove a local identification property that we apply, in combination with a convergence hypothesis, to get an active set identification result. We then prove, in the nonconvex case, a novel O(1/ √k) convergence rate result and … Read more

    Proximity measures based on KKT points for constrained multi-objective optimization

  • Gabriele Eichfelder
  • Leo Warnow
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Multi-Criteria Optimization Tags , ,

    An important aspect of optimization algorithms, for instance evolutionary algorithms, are termination criteria that measure the proximity of the found solution to the optimal solution set. A frequently used approach is the numerical verification of necessary optimality conditions such as the Karush-Kuhn-Tucker (KKT) conditions. In this paper, we present a proximity measure which characterizes the … Read more

    On Constraint Qualifications for Second-Order Optimality Conditions Depending on a Single Lagrange Multiplier.

  • Gabriel Haeser
  • Alberto Ramos
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , ,

    Second-order optimality conditions play an important role in continuous optimization. In this paper, we present and discuss new constraint qualifications to ensure the validity of some well-known second-order optimality conditions. Our main interest is on second-order conditions that can be associated with numerical methods for solving constrained optimization problems. Such conditions depend on a single … Read more

    Data-compatibility of algorithms

  • Yair Censor
  • Maroun Zaknoon
  • Alexander J. Zaslavski
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , , , ,

    The data-compatibility approach to constrained optimization, proposed here, strives to a point that is “close enough” to the solution set and whose target function value is “close enough” to the constrained minimum value. These notions can replace analysis of asymptotic convergence to a solution point of infinite sequences generated by specific algorithms. We consider a … Read more

    Dynamic string-averaging CQ-methods for the split feasibility problem with percentage violation constraints arising in radiation therapy treatment planning

  • Mark Brooke
  • Yair Censor
  • Aviv Gibali
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , , , , ,

    In this paper we study a feasibility-seeking problem with percentage violation con- straints. These are additional constraints, that are appended to an existing family of constraints, which single out certain subsets of the existing constraints and declare that up to a speci ed fraction of the number of constraints in each subset is allowed to be … Read more

    An inexact augmented Lagrangian method for nonsmooth optimization on Riemannian manifold

  • Deng Kangkang
  • Peng Zheng
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization

    We consider a nonsmooth optimization problem on Riemannian manifold, whose objective function is the sum of a differentiable component and a nonsmooth convex function. We propose a manifold inexact augmented Lagrangian method (MIALM) for the considered problem. The problem is reformulated to a separable form. By utilizing the Moreau envelope, we get a smoothing subproblem … Read more

    Superiorization vs. Accelerated Convex Optimization: The Superiorized/Regularized Least-Squares Case

  • Yair Censor
  • Stefania Petra
  • Christoph Schnörr
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , ,

    In this paper we conduct a study of both superiorization and optimization approaches for the reconstruction problem of superiorized/regularized solutions to underdetermined systems of linear equations with nonnegativity variable bounds. Specifically, we study a (smoothed) total variation regularized least-squares problem with nonnegativity constraints. We consider two approaches: (a) a superiorization approach that, in contrast to … Read more

    Proximal Method for $\ell_0- based Sparse Enhanced Control Problems in Large-scale Interconnected Systems

  • Wah June Leong
  • Hong Seng Sim
  • Kok Lay Teo
  • Changzhi Wu
    • Categories Constrained Nonlinear Optimization, Systems governed by Differential Equations Optimization

    This paper considers linear quadratic optimal control problem of large-scale interconnected systems. An algorithmic framework is constructed to design controllers that provide a desired tradeoff between the system performance and the sparsity of the static feedback matrix. This is accomplished by introducing a minimization problem involving $\ell_0-$norm of the feedback matrix subject to a maximum … Read more