Nonlinear Optimization

A derivative-free trust-funnel method for equality-constrained nonlinear optimization

  • Phillipe Sampaio
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    In this work, we look into new derivative-free methods to solve equality-constrained optimization problems. Of particular interest, are the trust-region techniques, which have been investigated for the unconstrained and bound-constrained cases. For solving equality-constrained optimization problems, we introduce a derivative-free adaptation of the trust-funnel method combined with a self-correcting geometry scheme and present some encouraging … Read more

    A trust-region derivative-free algorithm for constrained optimization

  • Paulo Conejo
  • Elizabeth Wegner Karas
  • Lucas G. Pedroso
    • Categories Constrained Nonlinear Optimization

    We propose a trust-region algorithm for constrained optimization problems in which the derivatives of the objective function are not available. In each iteration, the objective function is approximated by a model obtained by quadratic interpolation, which is then minimized within the intersection of the feasible set with the trust region. Since the constraints are handled … Read more

    On Calmness of the Argmin Mapping in Parametric Optimization Problems

  • Diethard Klatte
  • Bernd Kummer
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization, Semi-infinite Programming Tags , , ,

    Recently, Canovas et. al. (2013) presented an interesting result: the argmin mapping of a linear semi-infinite program under canonical perturbations is calm if and only if some associated linear semi-infinite inequality system is calm. Using classical tools from parametric optimization, we show that the if-direction of this condition holds in a much more general framework … Read more

    Problem Formulations for Simulation-based Design Optimization using Statistical Surrogates and Direct Search

  • Michael Kokkolaras
  • Sébastien Le Digabel
  • Bastien Talgorn
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Nonsmooth Optimization

    Typical challenges of simulation-based design optimization include unavailable gradients and unreliable approximations thereof, expensive function evaluations, numerical noise, multiple local optima and the failure of the analysis to return a value to the optimizer. One possible remedy to alleviate these issues is to use surrogate models in lieu of the computational models or simulations and … Read more

    Improving direct search algorithms by multilevel optimization techniques

  • Emanuele Frandi
  • Alessandra Papini
    • Categories Nonlinear Optimization

    Direct Search algorithms are classical derivative-free methods for optimization. Though endowed with solid theoretical properties, they are not well suited for large-scale problems due to slow convergence and scaling issues. In this paper, we discuss how such limitations can be circumvented, on problems for which a hierarchy of objective functions is available, by using multilevel … Read more

    A Note on Lerner Index, Cross-Elasticity and Revenue Optimization Invariants

  • Alexander Kushkuley
  • Su-Ming Wu
    • Categories Applications - OR and Management Sciences, Nonlinear Optimization Tags , , , ,

    We study common properties of retail pricing models in a general framework of calculus of variations. In particular, we observe that for any demand model, optimal de-seasoned revenue rate divided by price elasticity is time invariant. We also obtain a generalization of a well known inverse relationship between price elasticity of demand and Lerner index. … Read more

    A Stochastic Quasi-Newton Method for Large-Scale Optimization

  • Richard H. Byrd
  • Samantha Hansen
  • Jorge Nocedal
  • Yoram Singer
    • Categories Data-Mining, Stochastic Programming, Unconstrained Optimization Tags , , ,

    Abstract The question of how to incorporate curvature information in stochastic approximation methods is challenging. The direct application of classical quasi- Newton updating techniques for deterministic optimization leads to noisy curvature estimates that have harmful effects on the robustness of the iteration. In this paper, we propose a stochastic quasi-Newton method that is efficient, robust … Read more

    Distributed Optimization Methods for Large Scale Optimal Control

  • Attila Kozma
    • Categories Optimization of Simulated Systems, Quadratic Programming Tags , , , , ,

    This thesis aims to develop and implement both nonlinear and linear distributed optimization methods that are applicable, but not restricted to the optimal control of distributed systems. Such systems are typically large scale, thus the well-established centralized solution strategies may be computationally overly expensive or impossible and the application of alternative control algorithms becomes necessary. … Read more

    On QPCCs, QCQPs and Completely Positive Programs

  • Lijie Bai
  • John E. Mitchell
  • Jong-Shi Pang
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Linear, Cone and Semidefinite Programming

    This paper studies several classes of nonconvex optimization problems defined over convex cones, establishing connections between them and demonstrating that they can be equivalently formulated as convex completely positive programs. The problems being studied include: a quadratically constrained quadratic program (QCQP), a quadratic program with complementarity constraints (QPCC), and rank constrained semidefinite programs. Our results … Read more

    Subset Selection by Mallows’ Cp: A Mixed Integer Programming Approach

  • Ryuhei Miyashiro
  • Yuichi Takano
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming, Statistics Tags , , ,

    This paper concerns a method of selecting the best subset of explanatory variables for a linear regression model. Employing Mallows’ C_p as a goodness-of-fit measure, we formulate the subset selection problem as a mixed integer quadratic programming problem. Computational results demonstrate that our method provides the best subset of variables in a few seconds when … Read more