Infinite Dimensional Optimization

ALESQP: An augmented Lagrangian equality-constrained SQP method for optimization with general constraints

  • Harbir Antil
  • Drew P. Kouri
  • Denis Ridzal
    • Categories Constrained Nonlinear Optimization, Infinite Dimensional Optimization, Nonlinear Optimization

    We present a new algorithm for infinite-dimensional optimization with general constraints, called ALESQP. In short, ALESQP is an augmented Lagrangian method that penalizes inequality constraints and solves equality-constrained nonlinear optimization subproblems at every iteration. The subproblems are solved using a matrix-free trust-region sequential quadratic programming (SQP) method that takes advantage of iterative, i.e., inexact linear … Read more

    On Solving Elliptic Obstacle Problems by Compact Abs-Linearization

  • Olga Weiß
  • Monika Weymuth
    • Categories Infinite Dimensional Optimization, Nonsmooth Optimization Tags , , , , , ,

    We consider optimal control problems governed by an elliptic variational inequality of the first kind, namely the obstacle problem. The variational inequality is treated by penalization which leads to optimization problems governed by a nonsmooth semi- linear elliptic PDE. The CALi algorithm is then applied for the efficient solution of these nonsmooth optimization problems. The … Read more

    Optimization with learning-informed differential equation constraints and its applications

  • Guozhi Dong
  • Michael Hintermueller
  • Kostas Papafitsoros
    • Categories Biomedical Applications, Infinite Dimensional Optimization, Nonlinear Optimization

    Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through data-driven techniques are studied. A particular focus is on the analysis and on numerical methods for problems with machine-learned components. For a rather general context, an error analysis … Read more

    A Structure Exploiting Algorithm for Non-Smooth Semi-Linear Elliptic Optimal Control Problems

  • Stephan Schmidt
  • Olga Weiß
  • Andrea Walther
    • Categories Infinite Dimensional Optimization, Nonsmooth Optimization

    We investigate optimization problems with a non-smooth partial differential equation as constraint, where the non-smoothness is assumed to be caused by Nemytzkii operators generated by the functions abs, min and max. For the efficient as well as robust solution of such problems, we propose a new optimization method based on abs-linearization, i.e., a special handling … Read more

    A Primal-Dual Algorithm for Risk Minimization

  • Drew P. Kouri
  • Thomas Surowiec
    • Categories Infinite Dimensional Optimization, Nonsmooth Optimization, Stochastic Programming Tags , , ,

    In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is … Read more

    Graph Recovery From Incomplete Moment Information

  • Didier Henrion
  • Jean-Bernard Lasserre
    • Categories Infinite Dimensional Optimization, Semi-definite Programming, Statistics Tags , , ,

    We investigate a class of moment problems, namely recovering a measure supported on the graph of a function from partial knowledge of its moments, as for instance in some problems of optimal transport or density estimation. We show that the sole knowledge of first degree moments of the function, namely linear measurements, is sufficient to … Read more

    Stokes, Gibbs and volume computation of semi-algebraic sets

  • Didier Henrion
  • Jean-Bernard Lasserre
  • Matteo Tacchi
    • Categories Infinite Dimensional Optimization, Semi-definite Programming Tags , ,

    We consider the problem of computing the Lebesgue volume of compact basic semi-algebraic sets. In full generality, it can be approximated as closely as desired by a converging hierarchy of upper bounds obtained by applying the Moment-SOS (sums of squares) methodology to a certain infinite-dimensional linear program (LP). At each step one solves a semidefinite … Read more

    The Strip Method for Shape Derivatives

  • Harbir Antil
  • Drew P. Kouri
  • Sean Hardesty
  • Denis Ridzal
    • Categories Infinite Dimensional Optimization, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs Tags , , , ,

    A major challenge in shape optimization is the coupling of finite element method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multiphysics problems involving legacy codes, where the costs of implementing and maintaining shape derivative capabilities are prohibitive. The volume and boundary methods are two approaches … Read more

    KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

  • Drew P. Kouri
  • Denis Ridzal
  • Ray Tuminaro
    • Categories Control Applications, Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the … Read more

    Optimal Learning for Structured Bandits

  • Negin Golrezaei
  • Bart Paul Gerard Van Parys
    • Categories Convex Optimization, Semi-infinite Programming, Stochastic Programming Tags , ,

    We study structured multi-armed bandits, which is the problem of online decision-making under uncertainty in the presence of structural information. In this problem, the decision-maker needs to discover the best course of action despite observing only uncertain rewards over time. The decision- maker is aware of certain structural information regarding the reward distributions and would … Read more