## A nonmonotone trust-region algorithm with nonmonotone penalty parameters for constrained optimization.(English)Zbl 1059.65053

The authors consider general nonlinear programming problems in the form $\min f(x) \quad\text{s.t. }c(x)= 0\quad\text{and }1\leq x\leq u.$ For these problems, a nonmonotone trust-region algorithm with nonmonotone penalty parameters is presented. The given algorithm combines an successive quadratic programming approach with a trust-region strategy to globalize the process. The global convergence theory for the given algorithm is developed without regularity assumptions. Numerical experiments are presented.

### MSC:

 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming 90C55 Methods of successive quadratic programming type
Full Text:

### References:

 [1] Burke, J.V., A sequential quadratic programming method for potentially infeasible mathematical programs, J. math. anal. appl., 138, 111-144, (1989) · Zbl 0719.90066 [2] Byrd, R.H.; Schnabel, R.B.; Shultz, G.A., A trust region algorithm for nonlinearly constrained optimization, SIAM J. numer. anal., 24, 1152-1170, (1987) · Zbl 0631.65068 [3] Chen, Z.W.; Han, J.Y.; Han, Q.M., A globally convergent trust region algorithm for optimization with general constraints and simple bounds, Acta math. appl. sinica, 15, 425-432, (1999) · Zbl 1052.90611 [4] Conn, A.R.; Gould, NIM.; Toint, Ph.L., A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds, SIAM J.numer. anal., 28, 545-572, (1991) · Zbl 0724.65067 [5] Daniel, J.W., On perturbations in systems of linear inequalities, SIAM J. numer. anal., 10, 299-307, (1973) · Zbl 0268.90039 [6] Deng, N.Y.; Xiao, Y.; Zhou, F.J., A nonmonotonic trust region algorithm, J. optim. theory appl., 76, 259-285, (1993) · Zbl 0797.90088 [7] El-Alem, M., A robust trust region algorithm with a nonmonotonic penalty parameter scheme for constrained optimization, SIAM J. optim., 5, 348-378, (1995) · Zbl 0828.65063 [8] Gomes, F.A.M.; Maciel, M.C.; Martinez, J.M., Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters, Math. prog., 84, 161-200, (1999) · Zbl 1050.90574 [9] W. Hock, K. Schittkowski, Test examples for nonlinear programming codes, in: Lecture Notes in Economics and Mathematics Systems, Vol. 187, Springer, Berlin, 1981. · Zbl 0452.90038 [10] Ke, X.W.; Han, J.Y., A nonmonotone trust region algorithm for equality constrained optimization, Sci. in China (ser. A), 38, 683-695, (1995) · Zbl 0835.90089 [11] Lasdon, L.S., Reduced gradient methods, (), 235-242 · Zbl 0589.90067 [12] Martinez, J.M.; Santos, S.A., A trust-region strategy for minimization on arbitrary domains, Math. prog., 68, 267-301, (1995) · Zbl 0835.90092 [13] E.O. Omojokun, Trust region algorithms for optimization with nonlinear equality and inequality constrains, Ph.D. Thesis, University of Colorado at Boulder, USA, 1989. [14] Powell, M.J.D.; Yuan, Y., A trust region algorithm for equality constrained optimization, Math. prog., 49, 189-211, (1991) · Zbl 0816.90121 [15] Schittkowski, K., The nonlinear programming method of Wilson, han and powell with an augmented Lagrangian type line search function, Numer. math., 38, 83-114, (1981) · Zbl 0534.65030 [16] Toint, Ph.L., A non-monotone trust region algorithm for nonlinear optimization subject to convex constraints, Math. prog., 77, 69-94, (1997) · Zbl 0891.90153
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.