Numerical Algebra, Control and Optimization (NACO)

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

Pages: 19 - 29, Volume 2, Issue 1, March 2012      doi:10.3934/naco.2012.2.19

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Chunlin Hao - Department of Applied Mathematics, Beijing University of Technology, Beijing 100124, China (email)
Xinwei Liu - Department of Applied Mathematics, Hebei University of Technology, Tianjin 300401, China (email)

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.

Keywords:  Overdetermined system of equations, sequential quadratical programming, global convergence.
Mathematics Subject Classification:  Primary: 90C30, 90C51; Secondary: 65K05.

Received: March 2011;      Revised: May 2011;      Available Online: March 2012.