Constrained Nonlinear Optimization

The solution of Euclidean norm trust region SQP subproblems via second order cone programs, an overview and elementary introduction

  • Florian Jarre
  • Felix Lieder
    • Categories Constrained Nonlinear Optimization, Second-Order Cone Programming Tags , ,

    It is well known that convex SQP subproblems with a Euclidean norm trust region constraint can be reduced to second order cone programs for which the theory of Euclidean Jordan-algebras leads to efficient interior-point algorithms. Here, a brief and self-contained outline of the principles of such an implementation is given. All identities relevant for the … Read more

    A polynomially solvable case of the pooling problem

  • Natashia Boland
  • Thomas Kalinowski
  • Fabian Rigterink
    • Categories Constrained Nonlinear Optimization

    Answering a question of Haugland, we show that the pooling problem with one pool and a bounded number of inputs can be solved in polynomial time by solving a polynomial number of linear programs of polynomial size. We also give an overview of known complexity results and remaining open problems to further characterize the border … Read more

    A DERIVATIVE-FREE APPROACH TO CONSTRAINED MULTIOBJECTIVE NONSMOOTH OPTIMIZATION

  • Giampaolo Liuzzi
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box. We define a linesearch-based solution method, and we show that it converges to a set of Pareto stationary points. To this … Read more

    Cutting Box Strategy: an algorithmic framework for improving metaheuristics for continuous global optimization

  • Marcia Fampa
  • Wendel Melo
  • Fernanda M. P. Raupp
    • Categories Constrained Nonlinear Optimization, Stochastic Approaches Tags , , ,

    In this work, we present a new framework to increase effectiveness of metaheuristics in seeking good solutions for the general nonlinear optimization problem, called Cutting Box Strategy (CBS). CBS is based on progressive reduction of the search space through the use of intelligent multi-starts, where solutions already obtained cannot be revisited by the adopted metaheuristic. … Read more

    Bounded perturbation resilience of projected scaled gradient methods

  • Yair Censor
  • Ming Jiang
  • Wenma Jin
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , ,

    We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected Newton method, … Read more

    On the non-ergodic convergence rate of an inexact augmented Lagrangian framework for composite convex programming

  • Xin Liu
  • Ya-Feng Liu
  • Shiqian Ma
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags ,

    In this paper, we consider the linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose an inexact augmented Lagrangian (IAL) framework for solving the problem. The stopping criterion used in solving the augmented Lagrangian (AL) subproblem in the proposed IAL framework is … Read more

    Discrete flow pooling problems in coal supply chains

  • Natashia Boland
  • Thomas Kalinowski
  • Fabian Rigterink
    • Categories (Mixed) Integer Nonlinear Programming, Constrained Nonlinear Optimization, Global Optimization Applications

    The pooling problem is a nonconvex nonlinear programming problem (NLP) with applications in the refining and petrochemical industries, but also the coal mining industry. The problem can be stated as follows: given a set of raw material suppliers (inputs) and qualities of the supplies, find a cost-minimising way of blending these raw materials in intermediate … Read more

    Evaluation complexity for nonlinear constrained optimization using unscaled KKT conditions and high-order models

  • Ernesto G. Birgin
  • José Mario Martínez
  • Sandra Augusta Santos
  • Philippe L. Toint
  • John L. Gardenghi
    • Categories Bound-constrained Optimization, Constrained Nonlinear Optimization Tags , , ,

    The evaluation complexity of general nonlinear, possibly nonconvex,constrained optimization is analyzed. It is shown that, under suitable smoothness conditions, an $\epsilon$-approximate first-order critical point of the problem can be computed in order $O(\epsilon^{1-2(p+1)/p})$ evaluations of the problem’s function and their first $p$ derivatives. This is achieved by using a two-phases algorithm inspired by Cartis, Gould, … Read more

    Global convergence of a derivative-free inexact restoration filter algorithm for nonlinear programming

  • Priscila Savulski Ferreira
  • Elizabeth Wegner Karas
  • Mael Sachine
  • Francisco N. C. Sobral
    • Categories Constrained Nonlinear Optimization Tags , , , , ,

    In this work we present an algorithm for solving constrained optimization problems that does not make explicit use of the objective function derivatives. The algorithm mixes an inexact restoration framework with filter techniques, where the forbidden regions can be given by the flat or slanting filter rule. Each iteration is decomposed in two independent phases: … Read more

    A special case of the generalized pooling problem arising in the mining industry

  • Natashia Boland
  • Thomas Kalinowski
  • Fabian Rigterink
  • Martin Savelsbergh
    • Categories Constrained Nonlinear Optimization, Global Optimization Applications

    Iron ore and coal are substantial contributors to Australia’s export economy. Both are blended products that are made-to-order according to customers’ desired product qualities. Mining companies have a great interest in meeting these target qualities since deviations generally result in contractually agreed penalties. This paper studies a variation of the generalized pooling problem (GPP) arising … Read more