A Note on Wedge Trust Region Radius Update

Abstract:

Wedge trust region method based on traditional trust region is designed for derivative free optimization problems. This method adds a constraint to the trust region problem, which is called “wedge method”. The problem is that the updating strategy of wedge trust region radius is somewhat simple. In this paper, we develop and combine a new radius updating rule with this method. For most test problems, the number of function evaluations is reduced significantly. The experiments demonstrate the effectiveness of the improvement through our algorithm.

• Periodical: Applied Mechanics and Materials (Volumes 52-54)
• Pages: 926-931
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.52-54.926
• Online since: March 2011
• Authors: Qing Hua Zhou, Feng Xia Xu, Yan Geng, Ya Rui Zhang
• Keywords: Derivative Free Optimization, Radius Update, Unconstrained Optimization, Wedge Trust Region

References

[1] A.R. Coon, K. Scheinberg, and Ph.L. Toint: Recent progress in unconstrained nonlinear optimization without derivatives, Mathematical Programming, 79, pp.397-414 (1997).

DOI: 10.1007/bf02614326

[2] M.J.D. Powell: Direct search algorithms for optimization calculations, Acta Numerica, 7, pp.287-336 (1998).

DOI: 10.1017/s0962492900002841

[3] M. Marazzi and J. Nocedal: Wedge trust region methods for derivative free optimization, Math. Program., Series A, 91, p.289–305 (2002).

DOI: 10.1007/s101070100264

[4] A.R. Conn, K. Scheinberg, and L. Vicente: Geometry of interpolation sets in derivative free optimization, Mathematical Programming, Series A, 111, p.141–172 (2007).

DOI: 10.1007/s10107-006-0073-5

[5] G. Fasano, J.L. Morales and J. Nocedal: On the geometry phase in model-based algorithms for derivative-free optimization, Optimization Methods & Software, Vol 24, issue 1, pp.145-154, (2009).

DOI: 10.1080/10556780802409296

[6] A.R. Conn, K. Scheinberg, and L.N. Vicente: Global convergence of general derivative-free trust-region algorithms to first- and second-order critical points, SIAM J. Optim., 20(1), p.387–415 (2009).

DOI: 10.1137/060673424

[7] M.J.D. Powell: New developments of NEWUOA for minimization without derivatives, Tech. Rep. DAMPT 2007/NA05, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, (2007).

[8] J.L. Morales: A trust region based algorithm for unconstrained derivative–free optimization, Tech. Rep., Departamento de Matemáticas, ITAM, (2007).

[9] J.J. Moré and D.C. Sorensen: Computing a trust region step, SIAM Journal on Scientific and Statistical Computing, 4, pp.553-572 (1983).

DOI: 10.1137/0904038

[10] Jéròme M.B. Walmag, and éric J.M. Delhez: A note on trust-region radius update, SIAM J. Optim., 16(2), pp.548-582 (2005).

DOI: 10.1137/030602563

[11] I. Bongartz, A.R. Conn, N.I.M. Gould, and Ph. L. Toint: CUTE: Constrained and unconstrained testing environment, ACM Transactions on Mathematical Software, 21(1), pp.123-160 (1995).

DOI: 10.1145/200979.201043

[12] A.R. Conn, N.I.M. Gould, and P.L. Toint: Trust Region Methods, MPS/SIAM Ser. Optim. 1, SIAM, Philadelphia, (2000).

[13] L. Hei: A self-adaptive trust region algorithm, J. Comput. Math., 21, p.229–236 (2003).

[14] Information on http: /www. eecs. northwestern. edu/~nocedal/wedge. html.