Abstract
A new, robust recursive quadratic programming algorithm model based on a continuously differentiable merit function is introduced. The algorithm is globally and superlinearly convergent, uses automatic rules for choosing the penalty parameter, and can efficiently cope with the possible inconsistency of the quadratic search subproblem. The properties of the algorithm are studied under weak a priori assumptions; in particular, the superlinear convergence rate is established without requiring strict complementarity. The behavior of the algorithm is also investigated in the case where not all of the assumptions are met. The focus of the paper is on theoretical issues; nevertheless, the analysis carried out and the solutions proposed pave the way to new and more robust RQP codes than those presently available.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
DI PILLO, G., FACCHINEI, F., and GRIPPO, L., An RQP Algorithm Using a Differentiable Exact Penalty Function for Inequality Constrained Problems, Mathematical Programming, Vol. 55, pp. 49–68, 1992.
FACCHINEI, F., A New Recursive Quadratic Programming Algorithm with Global and Superlinear Convergence Properties, DIS Technical Report 12.93, Università di Roma “La Sapienza”, 1993.
LUCIDI, S., New Results on a Continuously Differentiable Penalty Function, SIAM Journal on Optimization, Vol. 2, pp. 558–574, 1992.
DI PILLO, G., and GRIPPO, L., An Exact Penalty Method with Global Convergence Properties for Nonlinear Programming Problems, Mathematical Programming, Vol. 36, pp. 1–18, 1986.
POWELL, M. J. D., and YUAN, Y., A Recursive Quadratic Programming Algorithm That Uses Differentiable Exact Penalty Functions, Mathematical Programming, Vol. 35, pp. 265–278, 1986.
POLYAK, B. T., Introduction to Optimization, Optimization Software, New York, New York, 1987.
BURKE, J. V., and HAN, S. H., A Robust Sequential Quadratic Programming Method, Mathematical Programming, Vol. 43, pp. 277–303, 1989.
BANK, B., GUDDATT, J., KLATTE, D., KUMMER, B., and TAMMER, K., Nonlinear Parametric Optimization, Birkhäuser, Basel, Switzerland, 1983.
BOGGS, P. T., TOLLE, J. W., and WANG, P., On the Local Convergence of Quasi-Newton Methods for Constrained Optimization, SIAM Journal on Control and Optimization, Vol. 20, pp. 161–171, 1982.
BONNANS, J. F., Rates of Convergence of Newton-Type Methods for Variational Inequalities and Nonlinear Programming, Applied Mathematics and Optimization, Vol. 29, pp. 161–186, 1994.
FACCHINEI, F., and LUCIDI, S., Quadratically and Superlinearly Convergent Algorithms for the Solution of Inequality Constrained Minimizations Problems, Journal of Optimization Theory and Applications, Vol. 85, pp. 265–289, 1995.
MIFFLIN, R., Semismooth and Semiconvex Functions in Constrained Optimization, SIAM Journal on Control and Optimization, Vol. 15, pp. 957–972, 1977.
QI, L., and SUN, J., A Nonsmooth Version of Newton's Method, Mathematical Programming, Vol. 58, pp. 353–368, 1993
FACCHINEI, F., Minimization of SC 1 -functions and the Maratos Effect, Operations Research Letters, Vol. 17, pp. 131–137, 1995.
BURKE, J. V., A Sequential Quadratic Programming Method for Potentially Infeasible Programs, Journal of Mathematical Analysis and Applications, Vol. 139, pp. 319–351, 1989.
BURKE J., A Robust Trust Region Method for Constrained Nonlinear Programming Problems, SIAM Journal on Optimization, Vol. 2, pp. 325–347, 1992.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Facchinei, F. Robust Recursive Quadratic Programming Algorithm Model with Global and Superlinear Convergence Properties. Journal of Optimization Theory and Applications 92, 543–579 (1997). https://doi.org/10.1023/A:1022655423083
Issue Date:
DOI: https://doi.org/10.1023/A:1022655423083