Global convergence of an SQP algorithm for nonlinearoptimization with overdetermined constraints

Chunlin Hao; Xinwei Liu

doi:10.3934/naco.2012.2.19

Article Contents

2012, Volume 2, Issue 1: 19-29. Doi: 10.3934/naco.2012.2.19

This issue Previous Article A smoothing Newton method for generalized Nash equilibrium problems with second-order cone constraints Next Article A sixth order numerical method for a class of nonlinear two-point boundary value problems

Global convergence of an SQP algorithm for nonlinear optimization with overdetermined constraints

Chunlin Hao^1, and
Xinwei Liu^2,

1.
Department of Applied Mathematics, Beijing University of Technology, Beijing 100124
2.
Department of Applied Mathematics, Hebei University of Technology, Tianjin 300401

Received: March 2011

Revised: May 2011

Published: March 2012

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Abstract

A sequential quadratic programming (SQP) algorithm is presented for solving nonlinear optimization with overdetermined constraints. In each iteration, the quadratic programming (QP) subproblem is always feasible even if the gradients of constraints are always linearly dependent and the overdetermined constraints may be inconsistent. The $\ell_2$ exact penalty function is selected as the merit function. Under suitable assumptions on gradients of constraints, we prove that the algorithm will terminate at an approximate KKT point of the problem, or there is a limit point which is either a point satisfying the overdetermined system of equations or a stationary point for minimizing the $\ell_2$ norm of the residual of the overdetermined system of equations.

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Mathematics Subject Classification: Primary: 90C30, 90C51; Secondary: 65K05.

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