International Conference «Inverse and Ill-Posed Problems of Mathematical Physics»,
dedicated to Professor M.M. Lavrent’ev in occasion of his 75-th birthday, August 20-25, 2007, Novosibirsk,
Russia
Intel® MKL-based Trust-Region Solvers: Performance and Applications in Geosciences
Nikolay I. Gorbenko*, Alexander V. Avdeev*, Nikita A. Shustrov*
Intel Corporation R&D Lab, Novosibirsk, Russia, e-mail: nikolay.i.gorbenko@intel.com
Trust-Region (TR) algorithms are relatively new iterative algorithms for solving nonlinear optimization
problems. High efficiency of TR methods was demonstrated in a number of recent papers and books [1].
They have better local super convergence, when compared to Newton-type methods, commonly used for
solving Inverse Problems [2]. TR techniques are used in a number of well-known SW libraries such as
IMSL, TAO, GALAHAD, LANCELOT, etc.
Highly-optimized Trust-Region solvers developed for Intel® Math Kernel Library [3] allow to solve:
– nonlinear least squares problem (without and with bound constraints)
– system of nonlinear equations (without and with bound constraints)
– problem of functional’s minimization (without constraints)
The auxiliary routines provide calculation of Jacoby and Hessian matrices as well as gradient vector. TR
solvers are implemented with OpenMP support and can be used in multiprocessing mode. They show
excellent performance vs. competitors (VNI IMSL Fortran library v5.0 and TAO v1.8.1) - on benchmark
tests TR give average 10 times speed-ups vs. IMSL and 5 times average speed-ups vs. TAO.
TR effective usage in a number of applied geophysical problems will be presented.
REFERENCES
1. A. R. Conn, N. I.M. Gould, P. L. Toint. Trust-Region Methods. SIAM Society for Industrial & Applied
Mathematics, Englewood Cliffs, New Jersey, 2000.
2. M.M.Lavrentiev, A.V.Avdeev, M.M.Lavrentiev, Jr., V.I.Priimenko. Inverse Problems of Mathematical
Physics. VSP Publ., The Netherlands, 2003.
3. Intel® Math Kernel Library - http://www.intel.com/cd/software/products/asmona/eng/perflib/mkl/index.htm