Institute of Computational Mathematics and Mathematical Geophysics SB RAS

Тезисы докладов

Высокопроизводительные вычисления, параллельные методы и алгоритмы в задачах геофизики

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. They have global convergence and local super convergence, which differ them from line search methods, used quite often for solving Inverse Problems. TR techniques is implemented in a number of well-known SW libraries such as IMSL, TAO, GALAHAD, LANCELOT, etc. Let us explain the main difference of TR method from classical Newton one. Assume we have a current guess of the solution for the optimization problem. An approximate model can be constructed near the current point. Solution of the approximate model can be taken as the next iterate point. The classical line search algorithms also solve approximate models to obtain search directions. However, in TR algorithms, the approximation model is only “trusted” in the region near current iterate. This seems reasonable, because for general nonlinear functions local approximate models (such as linear and quadratic approximations) can only fit the original function locally. The region that the approximate model is trusted is called “trust region”. The trust region is adjusted from iteration to iteration, i.e. if computations indicate the approximation model fit the original problem quite well, the trust region can be enlarged. Otherwise when the approximation works not good enough the trust region will be reduced. TR solvers developed and implemented by the authors are based on Intel MKL (Math Kernel Library). There are versions of TR for Intel IA32, EM64T, IA64 platforms (Windows and Linux operating systems). In addition to Fortran-interface, TR solvers include C-language interface for all functions and routines. TR solvers are implemented with OpenMP support and can be used in multiprocessing mode. Keywords Nonlinear optimization, Trust-Region solvers, Intel MKL, Oil & Gas Problems

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