Sven Leyffer

Using Filter Methods to Guide Convergence for ADMM, with Applications to Nonnegative Matrix Factorization Problems

  • Robert Baraldi
  • Stefan M. Wild
  • Sven Leyffer
    • Categories Applications - Science and Engineering, Nonlinear Optimization Tags , , ,

    Nonconvex, nonlinear cost functions arise naturally in physical inverse problems and machine learning. The alternating direction method of multipliers (ADMM) has seen extensive use in these applications, despite exhibiting uncertain convergence behavior in many practical nonconvex settings, and struggling with general nonlinear constraints. In contrast, filter methods have proved effective in enforcing convergence for sequential … Read more

    Switching Time Optimization for Binary Quantum Optimal Control

  • Xinyu Fei
  • Lucas Brady
  • Jeffrey Larson
  • Sven Leyffer
  • Siqian Shen
    • Categories (Mixed) Integer Nonlinear Programming, Basic Sciences Applications, Control Applications Tags , ,

    Quantum optimal control is a technique for controlling the evolution of a quantum system and has been applied to a wide range of problems in quantum physics. We study a binary quantum control optimization problem, where control decisions are binary-valued and the problem is solved in diverse quantum algorithms. In this paper, we utilize classical … Read more

    Modeling Design and Control Problems Involving Neural Network Surrogates

  • Dominic Yang
  • Prasanna Balaprakash
  • Sven Leyffer
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications, Nonsmooth Optimization Tags , , , ,

    We consider nonlinear optimization problems that involve surrogate models represented by neural net-works. We demonstrate first how to directly embed neural network evaluation into optimization models, highlight a difficulty with this approach that can prevent convergence, and then characterize stationarity of such models. We then present two alternative formulations of these problems in the specific … Read more

    Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics

  • Prasanna Balaprakash
  • Sven Leyffer
  • Jongeun Kim
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering Tags , , ,

    In this paper we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. The symbolic regression problem can be formulated as … Read more

    Compact Representations of Structured BFGS Matrices

  • Johannes Brust
  • Sven Leyffer
  • Zichao (Wendy) Di
  • Cosmin G. Petra
    • Categories Nonlinear Optimization Tags , , , ,

    For general large-scale optimization problems compact representations exist in which recursive quasi-Newton update formulas are represented as compact matrix factorizations. For problems in which the objective function contains additional structure, so-called structured quasi-Newton methods exploit available second-derivative information and approximate unavailable second derivatives. This article develops the compact representations of two structured Broyden-Fletcher-Goldfarb-Shanno update formulas. … Read more

    Binary Optimal Control by Trust-Region Steepest Descent

  • Mirko Hahn
  • Sven Leyffer
  • Sebastian Sager
    • Categories Distributed Control, Integer Programming, Systems governed by Differential Equations Optimization Tags , ,

    We present a trust-region steepest descent method for dynamic optimal control problems with binary-valued integrable control functions. Our method interprets the control function as an indicator function of a measurable set and makes set-valued adjustments derived from the sublevel sets of a topological gradient function. By combining this type of update with a trust-region framework, … Read more

    A Mixed-Integer PDE-Constrained Optimization Formulation for Electromagnetic Cloaking

  • Sven Leyffer
  • Todd S. Munson
  • Ryan Vogt
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Optimization of Systems modeled by PDEs Tags , , ,

    We formulate a mixed-integer partial-differential equation constrained optimization problem for designing an electromagnetic cloak governed by the 2D Helmholtz equation with absorbing boundary conditions. Our formulation is an alternative to the topology optimization formulation of electromagnetic cloaking design. We extend the formulation to include uncertainty with respect to the angle of the incidence wave, and … Read more

    Inversion of Convection-Diffusion Equation with Discrete Sources

  • Mirko Hahn
  • Sven Leyffer
  • Bart van Bloemen Waanders
  • Lars Ruthotto
  • Meenarli Sharma
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization

    We present a convection-diffusion inverse problem that aims to identify an unknown number of sources and their locations. We model the sources using a binary function, and we show that the inverse problem can be formulated as a large-scale mixed-integer nonlinear optimization problem. We show empirically that current state-of-the-art mixed-integer solvers cannot solve this problem … Read more

    A Solution Framework for Linear PDE-Constrained Mixed-Integer Problems

  • Armin Fügenschuh
  • Sven Leyffer
  • Fabian Gnegel
  • Michael Hagel
  • Marcus Stiemer
    • Categories (Mixed) Integer Linear Programming, Control Applications, Network Optimization Tags , , , , ,

    We present a general numerical solution method for control problems with PDE-defined state variables over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs (and if necessary a linearization scheme) to derive constraints for a mixed-integer linear program (MILP) … Read more

    A Bilevel Approach for Identifying the Worst Contingencies for Nonconvex Alternating Current Power Systems

  • Brian Dandurand
  • Kibaek Kim
  • Sven Leyffer
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Robust Optimization Tags , , ,

    We address the bilevel optimization problem of identifying the most critical attacks to an alternating current (AC) power flow network. The upper-level binary maximization problem consists in choosing an attack that is treated as a parameter in the lower-level defender minimization problem. Instances of the lower-level global minimization problem by themselves are NP-hard due to … Read more