A Globally and Superlinearly Convergent SQP Algorithm for Nonlinear Constrained Optimization

Based on a continuously differentiable exact penalty function and a regularization technique for dealing with the inconsistency of subproblems in the SQP method, we present a new SQP algorithm for nonlinear constrained optimization problems. The proposed algorithm incorporates automatic adjustment rules for the choice of the parameters and makes use of an approximate directional derivative of the merit function to avoid the need to evaluate second order derivatives of the problem functions. Under mild assumptions the algorithm is proved to be globally convergent, and in particular the superlinear convergence rate is established without assuming that the strict complementarity condition at the solution holds. Numerical results reported show that the proposed algorithm is promising.

[1]  Stephen M. Robinson,et al.  Strongly Regular Generalized Equations , 1980, Math. Oper. Res..

[2]  Stefano Lucidi,et al.  New Results on a Continuously Differentiable Exact Penalty Function , 1992, SIAM J. Optim..

[3]  Francisco Facchinei,et al.  Robust Recursive Quadratic Programming Algorithm Model with Global and Superlinear Convergence Properties , 1997 .

[4]  Philip E. Gill,et al.  Numerically stable methods for quadratic programming , 1978, Math. Program..

[5]  D. Mayne,et al.  Exact penalty function algorithm with simple updating of the penalty parameter , 1991 .

[6]  Francisco Facchinei,et al.  Minimization of SC1 functions and the Maratos effect , 1995, Oper. Res. Lett..

[7]  E. Panier,et al.  A superlinearly convergent feasible method for the solution of inequality constrained optimization problems , 1987 .

[8]  James V. Burke,et al.  A robust sequential quadratic programming method , 1989, Math. Program..

[9]  M. J. D. Powell,et al.  A fast algorithm for nonlinearly constrained optimization calculations , 1978 .

[10]  Klaus Schittkowski,et al.  More test examples for nonlinear programming codes , 1981 .

[11]  Torkel Glad,et al.  A multiplier method with automatic limitation of penalty growth , 1979, Math. Program..

[12]  Peter Spellucci,et al.  A new technique for inconsistent QP problems in the SQP method , 1998, Math. Methods Oper. Res..

[13]  Jorge J. Moré,et al.  Computing a Trust Region Step , 1983 .

[14]  Paul T. Boggs,et al.  Sequential Quadratic Programming , 1995, Acta Numerica.

[15]  Yin Zhang,et al.  An SQP Augmented Lagrangian BFGS Algorithm for Constrained Optimization , 1992, SIAM J. Optim..

[16]  Kaoru Tone,et al.  Revisions of constraint approximations in the successive QP method for nonlinear programming problems , 1983, Math. Program..

[17]  Liqun Qi,et al.  A nonsmooth version of Newton's method , 1993, Math. Program..

[18]  J. Burke A sequential quadratic programming method for potentially infeasible mathematical programs , 1989 .