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By I. D. L. Bogle, J. Zilinskas

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Standard parts of branch and bound algorithm are implemented in the template and only method specific rules should be implemented by the user. Parallel programs 28 M. Baravykaite and J. iilinskas can b e obtained automatically using sequential program implemented using the template. References 1. E. Alba, F. , MALLBA: A Library of Skeletons for Combinatorical Optimization, Departamento de Lengua jes y Ciencias de la Computation Universidad de Malaga, ALCOMFT-TR-02-120, (2001). 2. M. Baravykaite, R.

3) \ 0 0 ... xj since a change of variables can always achieve this form. The gradient of f(x) is g{x) = Ax — b. Rate of Convergence of the Steepest Descent Optimisation Algorithm with Relaxation 51 We can also assume that x* = 0 (otherwise the substitution x — x* —» x can be made). Gradient algorithms then take the following general form x(k+i) = x(k) _ a(k)g(k) (4) where a^ is the step length at iteration k and gW = Ax^ — b. ), algorithms of this type can be related to dynamical systems. Once in this form, information about the asymptotic rates of convergence of the algorithms can be more readily obtainable.

Usually, SPSA requires that MAE be computed several hundred times that is reasonable for interactive Heston model calibration. Figure 3 below illustrates the applicability of the SPSA algorithm in practice, where we can see the dependence of MAE on the number of computations of function values compared with the same dependence obtained by the SFDA method. 36 V. Bartkuti and L. Sakalauskas Finite difference 2 10 Nurrijer of iterations Figure 3. Minimization of MAE by SPSA and SFDA methods. 2. Optimal Design of Cargo Oil Tankers In cargo oil tankers design, it is necessary to choose such sizes for bulkheads, that the weight of bulkheads would be minimal.

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