×

A modified QP-free feasible method. (English) Zbl 1217.90150

Summary: We present a modified QP-free filter method based on a new piecewise linear NCP functions. In contrast with the existing QP-free methods, each iteration in this algorithm only needs to solve systems of linear equations which are derived from the equality part in the KKT first order optimality conditions. Its global convergence and local superlinear convergence are obtained under mild conditions.

MSC:

90C30 Nonlinear programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Boggs, P. T.; Tolle, J. W.; Wang, P., On the local convergence of qusi-newton methods for constrained optimization, SIAM J. Control Optim., 20, 161-171 (1982) · Zbl 0494.65036
[2] Bonnons, J. F.; Painer, E. R.; Titts, A. L.; Zhou, J. L., Avoiding the Maratos effect by means of nonmontone linesearch Inequality constrained problems-feasible iterates, SIAM J. Numer Anal., 29, 1187-1202 (1922)
[3] Facchinei, F.; Lucidi, S., Quadraticly and superlinearly convergent for the solution of inequality constrained optimization problem, J. Optim. Theory Appl., 85, 265-289 (1995) · Zbl 0830.90125
[4] Fletcher, R.; Leyffer, S., Nonlinear programming without a penalty function, Math. Program., 91, 239-269 (2002) · Zbl 1049.90088
[5] Han, S. P., Superlinearly convergence variable metric algorithm for general nonlinear programming problems, Math. Program., 11, 263-282 (1976)
[6] Powell, M. J.D., A fast algorithm for nonlinear constrained optimization calculations, (Waston, G. A., Numerical Analysis (1978), Springer-Verlag: Springer-Verlag Berlin), 144-157 · Zbl 0453.90081
[7] Powell, M. J.D., Variable metric methods for constrained optimization, (Bachen, A.; etal., Mathematical Programming-The state of Art (1982), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0413.90065
[8] Zhu, Z. B.; Zhang, K. C.; Jian, J. B., An improved SQP algorithm for inequality constrained optimization, Math. Methods Oper. Res., 58, 271-282 (2003) · Zbl 1067.90160
[9] Panier, E. R.; Tits, A. L.; Herskovits, J. N., A QP-free, globally, locally superlinear convergent method for the inequality constrained optimizaiton problems, SIAM J. Control Optim., 36, 788-811 (1988) · Zbl 0651.90072
[10] Qi, H.; Qi, L., A new QP-free, globally V, locally superlinear convergent feasible method for the solution of inequality constrained optimization problems, SIAM J. Optim., 11, 113-132 (2000) · Zbl 0999.90038
[11] Zhou, Y.; Pu, D. G., A new QP-free feasible method for inequality constrained optimization, Math. Methods Oper. Res., 11, 31-43 (2007)
[12] Fletcher, R.; Leyffer, S.; Toint, P. L., On the global convergence of a filter-SQP algorithm, SIAM J. Optim., 13, 44-59 (2002) · Zbl 1029.65063
[13] Nie, P. Y.; Ma, C. F., A trust region filter method for general nonlinear programming, Appl. Math. Comput., 172, 1000-1017 (2006) · Zbl 1094.65060
[14] Facchinei, F.; Lucidi, S., Quadraticly and superlinearly convergent for the solution of inequality constrained optimization problem, JOTA, 85, 265-289 (1995) · Zbl 0830.90125
[15] Hock, W.; Schittkowski, K., Test examples for nonlinear programming codes, Lecture Notes in Econom and Math Systems, vol. 87 (1981), Springer-Verlag: Springer-Verlag Berlin · Zbl 0452.90038
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.