Nonlinear Programming 4

Nonlinear Programming 4

Proceedings of the Nonlinear Programming Symposium 4 Conducted by the Computer Sciences Department at the University of Wisconsin–Madison, July 14-16, 1980

1st Edition - January 28, 1981

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  • Editors: Olvi L. Mangasarian, Robert R. Meyer, Stephen M. Robinson
  • eBook ISBN: 9781483260174

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Nonlinear Programming, 4 focuses on linear, quadratic, and nonlinear programming, unconstrained minimization, nonsmooth and discrete optimization, ellipsoidal methods, linear complementarity problems, and software evaluation. The selection first elaborates on an upper triangular matrix method for quadratic programming, solving quadratic programs by an exact penalty function, and QP-based methods for large-scale nonlinearly constrained optimization. Discussions focus on large-scale linearly constrained optimization, search direction for superbasic variables, finite convergence, basic properties, comparison of three active set methods, and QP-based methods for dense problems. The book then examines an iterative linear programming algorithm based on an augmented Lagrangian and iterative algorithms for singular minimization problems. The publication ponders on the derivation of symmetric positive definite secant updates, preconditioned conjugate gradient methods, and finding the global minimum of a function of one variable using the method of constant signed higher order derivatives. Topics include effects of calculation errors, application to polynomial minimization, using moderate additional storage, updating Cholesky factors, and utilizing sparse second order information. The selection is a valuable source of data for researchers interested in nonlinear programming.

Table of Contents

  • Contributors


    An Upper Triangular Matrix Method for Quadratic Programming

    Solving Quadratic Programs by an Exact Penalty Function

    QP-Based Methods for Large-Scale Nonlinearly Constrained Optimization

    Numerical Experiments with an Exact L1 Penalty Function Method

    An Iterative Linear Programming Algorithm Based on an Augmented Lagrangian

    Iterative Algorithms for Singular Minimization Problems

    A New Derivation of Symmetric Positive Definite Secant Updates

    On Preconditioned Conjugate Gradient Methods

    Finding the Global Minimum of a Function of One Variable Using the Method of Constant Signed Higher Order Derivatives

    On a Bundle Algorithm for Nonsmooth Optimization

    Convergence Results in a Class of Variable Metric Subgradient Methods

    Monotropic Programming: Descent Algorithms and Duality

    Approximation and Convergence in Nonlinear Optimization

    Upper Planes of Quadratic 0-1 Functions and Stability in Graphs

    On the Existence of Fast Approximation Schemes

    Polynomially Bounded Ellipsoid Algorithms for Convex Quadratic Programming

    The Implicit Complementarity Problem

    Methods for Evaluating Nonlinear Programming Software


Product details

  • No. of pages: 560
  • Language: English
  • Copyright: © Academic Press 1981
  • Published: January 28, 1981
  • Imprint: Academic Press
  • eBook ISBN: 9781483260174

About the Editors

Olvi L. Mangasarian

Robert R. Meyer

Stephen M. Robinson

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