eldo_user

Optimization
Eldo Optimizer/Search Algorithm
Note
Specifying an appropriate tolerance on feasibility TOL_FEAS may lead to several savings
by enabling the optimization procedure to terminate when the difference between function
values along the search direction becomes as small as the absolute error in the values.
Computation of Finite-Difference Derivatives
One of the most demanding phases in terms of simulation is the computation of derivatives. The
Eldo optimizer uses finite differences; an approach to calculating the approximate derivatives
coming from Taylor’s theorem. Like many software tools, the Eldo optimizer performs
automatic calculation of finite differences whenever the simulator is unable to supply the code
to compute exact derivatives.
A popular formula for approximating the partial derivative ∂F/∂x at a given point is forward
differences or one-sided differences. The parameter h f controls the interval used to estimate the
gradients of the function F by forward differences:
One-sided difference estimates are used to ensure feasibility with respect to an upper or lower
bound on x. If x is close to an upper bound, the trial intervals will be negative. The final interval
is always positive.
• An approximation to the derivative of F is obtained by evaluating the function F at N + 1
points and performing some elementary arithmetic.
• The resulting gradient estimates should be accurate to O(h f ) unless the functions are
badly scaled.
Related Topics
Eldo Optimizer/Search Algorithm
Eldo Optimizer/Search Algorithm
The Search method is efficient for solving minimization optimization problems that are onedimensional.
This method belongs to the class of derivative free optimization (DFO) algorithms that are
dedicated to solving problems having one variable and one extracted measure. The Dichotomy
and Secant methods also belong to this class. The search method runs faster than the Dichotomy
method and is more robust than the modified Dichotomy (the Eldo optimizer/Secant) method.
Search is based on two distinct algorithms: FIND_ZERO and FIND_MINIMUM.
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Eldo® User's Manual, 15.3