A trust-region filter-SQP method for mathematical programs with linear complementarity constraints
Chunlin Hao Xinwei Liu
Journal of Industrial & Management Optimization 2011, 7(4): 1041-1055 doi: 10.3934/jimo.2011.7.1041
A trust-region filter-SQP method for mathematical programs with linear complementarity constraints (MPLCCs) is presented. The method is similar to that proposed by Liu, Perakis and Sun [Computational Optimization and Applications, 34, 5-33, 2006] but it solves the trust-region quadratic programming subproblems at each iteration and uses the filter technique to promote the global convergence. As a result, the method here is more robust since it admits the use of Lagrangian Hessian information and its performance is not affected by any penalty parameter. The preliminary numerical results on test problems generated by the QPECgen generator show that the presented method is effective.
keywords: filter-SQP Mathematical program with linear complementarity constraints trust-region method.
Global convergence of an SQP algorithm for nonlinear optimization with overdetermined constraints
Chunlin Hao Xinwei Liu
Numerical Algebra, Control & Optimization 2012, 2(1): 19-29 doi: 10.3934/naco.2012.2.19
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: sequential quadratical programming Overdetermined system of equations global convergence.

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