A gradient projection-multiplier method for nonlinear programming

  • J. T. Betts
Contributed Papers

Abstract

This paper 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.

Key Words

Multiplier method gradient projection method penalty function methods nonlinear programming parameter optimization 

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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • J. T. Betts
    • 1
  1. 1.Guidance and Control DivisionThe Aerospace CorporationEl Segundo

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