Infinite Dimensional Optimization

Barrier Methods Based on Jordan-Hilbert Algebras for Stochastic Optimization in Spin Factors

  • Baha Alzalg
    • Categories Infinite Dimensional Optimization, Linear, Cone and Semidefinite Programming, Stochastic Programming Tags , , , , ,

    We present decomposition logarithmic-barrier interior-point methods based on unital Jordan-Hilbert algebras for infinite-dimensional stochastic second-order cone programming problems in spin factors. The results show that the iteration complexity of the proposed algorithms is independent on the choice of Hilbert spaces from which the underlying spin factors are formed, and so it coincides with the best … Read more

    Different discretization techniques for solving optimal control problems with control complementarity constraints

  • Yu Deng
    • Categories Complementarity and Variational Inequalities, Infinite Dimensional Optimization Tags , , , ,

    There are first-optimize-then-discretize (indirect) and first-discretize-then-optimize (direct) methods to deal with infinite dimensional optimal problems numerically by use of finite element methods. Generally, both discretization techniques lead to different structures. Regarding the indirect method, one derives optimality conditions of the considered infinite dimensional problems in appropriate function spaces firstly and then discretizes them into suitable … Read more

    On the Weak and Strong Convergence of a Conceptual Algorithm for Solving Three Operator Monotone Inclusions

  • Yunier Bello-Cruz
  • Oday Hazaimah
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Infinite Dimensional Optimization Tags , , , ,

    In this paper, a conceptual algorithm modifying the forward-backward-half-forward (FBHF) splitting method for solving three operator monotone inclusion problems is investigated. The FBHF splitting method adjusts and improves Tseng’s forward-backward-forward (FBF) split- ting method when the inclusion problem has a third-part operator that is cocoercive. The FBHF method recovers the FBF iteration (when this aforementioned … Read more

    Recent Advances in Nonconvex Semi-infinite Programming: Applications and Algorithms

  • Hatim Djelassi
  • Alexander Mitsos
  • Oliver Stein
    • Categories Global Optimization Applications, Semi-infinite Programming

    The goal of this literature review is to give an update on the recent developments for semi-infinite programs (SIPs), approximately over the last 20 years. An overview of the different solution approaches and the existing algorithms is given. We focus on deterministic algorithms for SIPs which do not make any convexity assumptions. In particular, we … Read more

    Optimal Transport in the Face of Noisy Data

  • Bart Paul Gerard Van Parys
    • Categories Infinite Dimensional Optimization, Robust Optimization, Stochastic Programming Tags , ,

    Optimal transport distances are popular and theoretically well understood in the context of data-driven prediction. A flurry of recent work has popularized these distances for data-driven decision-making as well although their merits in this context are far less well understood. This in contrast to the more classical entropic distances which are known to enjoy optimal … Read more

    A Matrix-Free Trust-Region Newton Algorithm for Convex-Constrained Optimization

  • Drew P. Kouri
    • Categories Constrained Nonlinear Optimization, Infinite Dimensional Optimization, Nonlinear Optimization Tags , , , ,

    We describe a matrix-free trust-region algorithm for solving convex-constrained optimization problems that uses the spectral projected gradient method to compute trial steps. To project onto the intersection of the feasible set and the trust region, we reformulate and solve the dual projection problem as a one-dimensional root finding problem. We demonstrate our algorithm’s performance on … Read more

    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