A null-space primal-dual interior-point algorithm for nonlinear optimization with nice convergence properties

  • Xin-Wei Liu
  • Ya-xiang Yuan
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    We present a null-space primal-dual interior-point algorithm for solving nonlinear optimization problems with general inequality and equality constraints. The algorithm approximately solves a sequence of equality constrained barrier subproblems by computing a predictor step and a null space step in every iteration. The $\ell_2$ penalty function is taken as the merit function. Under very mild … Read more

    Hyperplane Arrangements with Large Average Diameter

  • Antoine Deza
  • Feng Xie
    • Categories Combinatorial Optimization, Polyhedra Tags , ,

    The largest possible average diameter of a bounded cell of a simple hyperplane arrangement is conjectured to be not greater than the dimension. We prove that this conjecture holds in dimension 2, and is asymptotically tight in fixed dimension. We give the exact value of the largest possible average diameter for all simple arrangements in … Read more

    An Augmented Primal-Dual Method for Linear Conic Programs

  • Florian Jarre
  • Franz Rendl
    • Categories Convex Optimization Tags , ,

    We propose a new iterative approach for solving linear programs over convex cones. Assuming that Slaters condition is satisfied, the conic problem is transformed to the minimization of a convex differentiable function. This “agumented primal-dual function” or “apd-function” is restricted to an affine set in the primal-dual space. The evaluation of the function and its … Read more

    Efficiency of Maximum Likelihood Estimators under Different Censored Sampling Schemes for Rayleigh Distribution

  • Abdallah Abd-Elfattah
  • Ziedan D. M.
  • Amal S. Hassan
    • Categories Applications - OR and Management Sciences, Statistics Tags

    The objective of this article is to study the effect of different types of censored sampling schemes on the estimation of the unknown parameter for Rayleigh distribution. The censored sampling schemes namely; type-I, type-II and progressive type-II censored sampling are to be considered. The comparisons made between the samples are based on the Fisher information, … Read more

    Approximate Primal Solutions and Rate Analysis in Dual Subgradient Methods

  • Angelia Nedich
  • Asuman Ozdaglar
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , ,

    We study primal solutions obtained as a by-product of subgradient methods when solving the Lagrangian dual of a primal convex constrained optimization problem (possibly nonsmooth). The existing literature on the use of subgradient methods for generating primal optimal solutions is limited to the methods producing such solutions only asymptotically (i.e., in the limit as the … Read more

    A new method for solving linear fractional programming problems

  • Said Tantawy
    • Categories Other Topics

    In this paper a new method is suggested for solving the problem in which the objective function is a linear fractional function, and where the constraint functions are in the form of linear inequalities. The proposed method is based mainly upon solving this problem algebraically using the concept of duality. Since the earlier methods based … Read more

    An estimation-free, robust conditional value-at-risk portfolio allocation model

  • Carlos Jabbour
  • Javier F. Peña
  • Juan C. Vera
  • Luis F. Zuluaga
    • Categories Finance and Economics, Robust Optimization, Semi-infinite Programming

    We propose a novel optimization model for risk-averse investors to obtain robust solutions for portfolio allocation problems. Unlike related models in the literature, no historical data or statistical estimation techniques are used to compute the parameters of the model. Instead, the parameters are directly obtained from current prices of options on the assets being considered. … Read more

    A strengthened formulation for the open pit mine production scheduling problem

  • Natashia Boland
  • Gary Froyland
  • Christopher Fricke
    • Categories Applications - Science and Engineering Tags , ,

    We present a strengthened integer programming formulation for the open pit mine production scheduling problem, where the precedence and production constraints are combined to form 0-1 knapsack inequalities. Addition of corresponding knapsack cover inequalities decreases the computational requirements to obtain the optimal integer solution, in many cases by a significant margin. CitationThe University of Melbourne, … Read more

    Derivative Free Optimization Methods for Optimizing Stirrer Configurations

  • Bulent Karasozen
  • Michael Schaefer
  • Omur Ugur
  • Kerim Yapici
    • Categories Bound-constrained Optimization, Chemical Engineering Tags , , ,

    In this paper a numerical approach for the optimization of stirrer configurations is presented. The methodology is based on a flow solver, and a mathematical optimization tool, which are integrated into an automated procedure. The flow solver is based on the discretization of the incompressible Navier-Stokes equations by means of a fully conservative finite-volume method … Read more

    Survey of Derivative Free Optimization Methods based on Interpolation

  • Bulent Karasozen
    • Categories Bound-constrained Optimization, Chemical Engineering Tags , , ,

    In this survey article we give the basic description of the interpolation based derivative free optimization methods and their variants. We review the recent contributions dealing with the maintaining the geometry of the interpolation set, the management of the trust region radius and the stopping criteria. Derivative free algorithms developed for problems with some structure … Read more