A Gradient Projection-Multiplier Method for Nonlinear Programming.

Abstract

This report describes a gradient projection-multiplier method for solving the general nonlinear programming problem. The algorithm poses a sequence of unconstrained optimization problems which are solved using a new projection-like formula to define the search directions. The unconstrained minimization of the augmented objective function determines points where the gradient of the Lagrangian function is zero. Points satisfying the constraints are located by applying an unconstrained algorithm to a penalty function. New estimates of the Lagrange multipliers and basis constraints are made at points satisfying either a Lagrangian condition or a constraint satisfaction condition. The penalty weight is increased only to prevent cycling. The numerical effectiveness of the algorithm is demonstrated on a set of test problems. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 30, 1978
Accession Number
ADA049864

Entities

People

  • John T. Betts

Organizations

  • The Aerospace Corporation

Tags

Communities of Interest

  • C4I
  • Space
  • Weapons Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Algorithms
  • Computer Programming
  • Computer Programs
  • Computers
  • Convergence
  • Digital Computers
  • Engineering
  • Errors
  • Inequalities
  • Lagrangian Functions
  • Mathematical Programming
  • Nonlinear Programming
  • Optimization
  • Security
  • Test And Evaluation

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Control Systems Engineering.
  • Systems Analysis and Design