A smoothing QP-free infeasible method for nonlinear inequality constrained optimization
Tóm tắt
In this paper, a smoothing QP-free infeasible method is proposed for nonlinear inequality constrained optimization problems. This iterative method is based on the solution of nonlinear equations which is obtained by the multipliers and the smoothing Fisher-Burmeister function for the KKT first-order optimality conditions. Comparing with other QP-free methods, this method does not request the strict feasibility of iteration. In particular, this method is implementable and globally convergent without assuming the strict complementarity condition and the isolatedness of accumulation points. Furthermore, the gradients of active constraints are not requested to be linearly independent. Preliminary numerical results indicate that this smoothing QP-free infeasible method is quite promising.
Tài liệu tham khảo
citation_journal_title=Acta Numerica; citation_title=Sequential quadratic programming; citation_author=P. T. Boggs, J. W. Tolle; citation_volume=45; citation_publication_date=1995; citation_pages=1-51; citation_doi=10.1017/S0962492900002518; citation_id=CR1
citation_journal_title=Math Programming; citation_title=A robust sequential quadratic programming method; citation_author=J. V. Burke, S. P. Han; citation_volume=43; citation_publication_date=1989; citation_pages=227-303; citation_doi=10.1007/BF01582294; citation_id=CR2
citation_journal_title=Journal of Optimization Theory and Applications; citation_title=Exact penalty function algorithm with simple updating of the penalty parameter; citation_author=J. F. A. De, O. Pantoja, D. Q. Mayne; citation_volume=69; citation_publication_date=1991; citation_pages=441-467; citation_doi=10.1007/BF00940684; citation_id=CR3
citation_journal_title=SIAM J Control Optim; citation_title=A QP-free, globally, locally superlinear convergent method for the inequality constrained optimization problems; citation_author=E. R. Panier, A. L. Tits, J. N. Herskovits; citation_volume=36; citation_publication_date=1988; citation_pages=788-811; citation_doi=10.1137/0326046; citation_id=CR4
citation_journal_title=SIAM J Optim; citation_title=A new QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization; citation_author=H. Qi, L. Qi; citation_volume=11; citation_publication_date=2000; citation_pages=113-132; citation_doi=10.1137/S1052623499353935; citation_id=CR5
citation_journal_title=Optimization; citation_title=A special Newton-type optimization method; citation_author=A. Fischer; citation_volume=24; citation_publication_date=1992; citation_pages=269-284; citation_doi=10.1080/02331939208843795; citation_id=CR6
citation_journal_title=J Comput Math; citation_title=A QP-free feasible method; citation_author=D. Pu, Y. Zhou, H. Zhang; citation_volume=22; citation_publication_date=2004; citation_pages=651-660; citation_id=CR7
citation_journal_title=Math Prog; citation_title=A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities; citation_author=L. Qi, D. Sun, G. Zhou; citation_volume=87; citation_publication_date=2000; citation_pages=1-35; citation_id=CR8
citation_journal_title=J Comput Appl Math; citation_title=An inexact generalized Newton method for second order C-differentiable optimization; citation_author=D. Pu, J. Zhang; citation_volume=93; citation_publication_date=1998; citation_pages=107-122; citation_doi=10.1016/S0377-0427(98)00064-8; citation_id=CR9
citation_title=Test example for nonlinear programming Codes; citation_inbook_title=Lecture Notes in Econom and Math Systems 187; citation_publication_date=1981; citation_id=CR10; citation_author=W. Hock; citation_author=K. Schittkowski; citation_publisher=Springer-Verlag