nonlinear optimization

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

    A Generalized Worst-Case Complexity Analysis for Non-Monotone Line Searches

  • Geovani Nunes Grapiglia
  • Ekkehard Sachs
    • Categories Nonlinear Optimization Tags , , ,

    We study the worst-case complexity of a non-monotone line search framework that covers a wide variety of known techniques published in the literature. In this framework, the non-monotonicity is controlled by a sequence of nonnegative parameters. We obtain complexity bounds to achieve approximate first-order optimality even when this sequence is not summable. Article Download View … Read more

    Nonlinear Optimization of District Heating Networks

  • Richard Krug
  • Volker Mehrmann
  • Martin Schmidt
    • Categories Applications - Science and Engineering, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , , ,

    We develop a complementarity-constrained nonlinear optimization model for the time-dependent control of district heating networks. The main physical aspects of water and heat flow in these networks are governed by nonlinear and hyperbolic 1d partial differential equations. In addition, a pooling-type mixing model is required at the nodes of the network to treat the mixing … Read more

    Using interior point solvers for optimizing progressive lens models with spherical coordinates

  • Glòria Casanellas
  • Jordi Castro
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization Tags , , , ,

    Designing progressive lenses is a complex problem that has been previously solved by formulating an optimization model based on Cartesian coordinates. In this work a new progressive lens model using spherical coordinates is presented, and interior point solvers are used to solve this new optimization model. Although this results in a highly nonlinear, nonconvex, continuous … 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

    Planning for Dynamics under Uncertainty

  • Dicong Qiu
  • Karsh Tharyani
    • Categories Dynamic Programming, Systems governed by Differential Equations Optimization, Unconstrained Optimization Tags , ,

    Planning under uncertainty is a frequently encountered problem. Noisy observation is a typical situation that introduces uncertainty. Such a problem can be formulated as a Partially Observable Markov Decision Process (POMDP). However, solving a POMDP is nontrivial and can be computationally expensive in continuous state, action, observation and latent state space. Through this work, we … Read more

    Limited-Memory BFGS with Displacement Aggregation

  • Albert S. Berahas
  • Frank E. Curtis
  • Baoyu Zhou
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

    A displacement aggregation strategy is proposed for the curvature pairs stored in a limited-memory BFGS (a.k.a. L-BFGS) method such that the resulting (inverse) Hessian approximations are equal to those that would be derived from a full-memory BFGS method. This means that, if a sufficiently large number of pairs are stored, then an optimization algorithm employing … Read more

    High-Order Evaluation Complexity for Convexly-Constrained Optimization with Non-Lipschitzian Group Sparsity Terms

  • Xiaojun Chen
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Data-Mining, Statistics Tags , , , , ,

    This paper studies high-order evaluation complexity for partially separable convexly-constrained optimization involving non-Lipschitzian group sparsity terms in a nonconvex objective function. We propose a partially separable adaptive regularization algorithm using a $p$-th order Taylor model and show that the algorithm can produce an (epsilon,delta)-approximate q-th-order stationary point in at most O(epsilon^{-(p+1)/(p-q+1)}) evaluations of the objective … Read more

    Algorithms for the circle packing problem based on mixed-integer DC programming

  • Yoshiko Ikebe
  • Satoru Masuda
  • Takayuki Okuno
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences Tags , ,

    Circle packing problems are a class of packing problems which attempt to pack a given set of circles into a container with no overlap. In this paper, we focus on the circle packing problem proposed by L{\’o}pez et.al. The problem is to pack circles of unequal size into a fixed size circular container, so as … Read more

    A note on solving nonlinear optimization problems in variable precision

  • Serge Gratton
  • Philippe L. Toint
    • Categories Applications - Science and Engineering, Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags ,

    This short note considers an efficient variant of the trust-region algorithm with dynamic accuracy proposed Carter (1993) and Conn, Gould and Toint (2000) as a tool for very high-performance computing, an area where it is critical to allow multi-precision computations for keeping the energy dissipation under control. Numerical experiments are presented indicating that the use … Read more