Andreas Wächter

Andreas is a Professor in the Department of Industrial Engineering and Management Sciences at Northwestern University.

A Quadratically Convergent Sequential Programming Method for Second-Order Cone Programs Capable of Warm Starts

  • Xinyi Luo
  • Andreas Wächter
    • Categories Constrained Nonlinear Optimization, Second-Order Cone Programming Tags , ,

    We propose a new method for linear second-order cone programs. It is based on the sequential quadratic programming framework for nonlinear programming. In contrast to interior point methods, it can capitalize on the warm-start capabilities of active-set quadratic programming subproblem solvers and achieve a local quadratic rate of convergence. In order to overcome the non-differentiability … Read more

    Exploiting Prior Function Evaluations in Derivative-Free Optimization

  • Frank E. Curtis
  • Shima Dezfulian
  • Andreas Wächter
    • Categories Bound-constrained Optimization, Nonlinear Optimization Tags , ,

    A derivative-free optimization (DFO) algorithm is presented. The distinguishing feature of the algorithm is that it allows for the use of function values that have been made available through prior runs of a DFO algorithm for solving prior related optimization problems. Applications in which sequences of related optimization problems are solved such that the proposed … Read more

    Solving Chance-Constrained Problems via a Smooth Sample-Based Nonlinear Approximation

  • James R. Luedtke
  • Alejandra Pena-Ordieres
  • Andreas Wächter
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , , , , ,

    We introduce a new method for solving nonlinear continuous optimization problems with chance constraints. Our method is based on a reformulation of the probabilistic constraint as a quantile function. The quantile function is approximated via a differentiable sample average approximation. We provide theoretical statistical guarantees of the approximation, and illustrate empirically that the reformulation can … Read more

    Sample Average Approximation with Adaptive Importance Sampling

  • Mingbin Feng
  • Alvaro Maggiar
  • Jeremy Staum
  • Andreas Wächter
    • Categories Stochastic Programming Tags , , , ,

    We study sample average approximations under adaptive importance sampling in which the sample densities may depend on previous random samples. Based on a generic uniform law of large numbers, we establish uniform convergence of the sample average approximation to the true function. We obtain convergence of the optimal value and optimal solutions of the sample … Read more

    A Limited-Memory Quasi-Newton Algorithm for Bound-Constrained Nonsmooth Optimization

  • Nitish Shirish Keskar
  • Andreas Wächter
    • Categories Bound-constrained Optimization, Nonsmooth Optimization

    We consider the problem of minimizing a continuous function that may be nonsmooth and nonconvex, subject to bound constraints. We propose an algorithm that uses the L-BFGS quasi-Newton approximation of the problem’s curvature together with a variant of the weak Wolfe line search. The key ingredient of the method is an active-set selection strategy that … Read more

    Uniform Convergence of Sample Average Approximation with Adaptive Importance Sampling

  • Mingbin Feng
  • Alvaro Maggiar
  • Jeremy Staum
  • Andreas Wächter
    • Categories Stochastic Programming Tags , , , ,

    We study sample average approximations under adaptive importance sampling. Based on a Banach-space-valued martingale strong law of large numbers, we establish uniform convergence of the sample average approximation to the function being approximated. In the optimization context, we obtain convergence of the optimal value and optimal solutions of the sample average approximation. Citation Technical Report … Read more

    A Derivative-Free Trust-Region Algorithm for the Optimization of Functions Smoothed via Gaussian Convolution Using Adaptive Multiple Importance Sampling

  • Irina S Dolinskaya
  • Alvaro Maggiar
  • Jeremy Staum
  • Andreas Wächter
    • Categories Nonlinear Optimization

    In this paper we consider the optimization of a functional $F$ defined as the co nvolution of a function $f$ with a Gaussian kernel. We propose this type of objective function for the optimization of the output of complex computational simulations, which often present some form of deterministic noise and need to be smoothed for … Read more

    An Active-Set Quadratic Programming Method Based On Sequential Hot-Starts

  • Travis C. Johnson
  • Christian Kirches
  • Andreas Wächter
    • Categories Quadratic Programming Tags , , , , , , ,

    A new method for solving sequences of quadratic programs (QPs) is presented. For each new QP in the sequence, the method utilizes hot-starts that employ information computed by an active-set QP solver during the solution of the first QP. This avoids the computation and factorization of the full matrices for all but the first problem … Read more

    An Inexact Sequential Quadratic Optimization Algorithm for Nonlinear Optimization

  • Frank E. Curtis
  • Travis C. Johnson
  • Daniel P. Robinson
  • Andreas Wächter
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    We propose a sequential quadratic optimization method for solving nonlinear optimization problems with equality and inequality constraints. The novel feature of the algorithm is that, during each iteration, the primal-dual search direction is allowed to be an inexact solution of a given quadratic optimization subproblem. We present a set of generic, loose conditions that the … Read more

    More Branch-and-Bound Experiments in Convex Nonlinear Integer Programming

  • Pierre Bonami
  • Jon Lee
  • Sven Leyffer
  • Andreas Wächter
    • Categories (Mixed) Integer Nonlinear Programming

    Branch-and-Bound (B&B) is perhaps the most fundamental algorithm for the global solution of convex Mixed-Integer Nonlinear Programming (MINLP) problems. It is well-known that carrying out branching in a non-simplistic manner can greatly enhance the practicality of B&B in the context of Mixed-Integer Linear Programming (MILP). No detailed study of branching has heretofore been carried out … Read more