Optimization Golden-Section search

The golden section search is the optimization analog of a binary search. It is used for functions of a single variable, F a). It is faster than a random search, but the difference in computing time will be trivial unless the objective function is extremely hard to evaluate. 

Example 2.2.1 Optimal drug dosing by golden section search... 

Remark 1 Steps (i) and (ii) are applied to the overall HEN without decomposing it into subnetworks. It is assumed, however, that we have a fixed HRAT for which we calculated the minimum utility cost. The HRAT can be optimized by using the golden section search in the same way that we described it in Figure 8.20. 

The golden-section search method determines the optimal solution to a bounded objective function that is one-dimensional and unimodal. However, the function need not be continu-... 

The optimization problem is one-dimensional with a nonlinear objective function, which may be discontinuous, depending on the heat-exchanger area. The single decision variable is bounded. Therefore, the golden-section search is suitable for determining the optimal solution. The calculations can be carried out conveniently in the following manner for each selection of rLGo,out ... 

Golden-section search. Use 10 steps of the golden-section search method to find the optimal dimensions for the cylindrical reactor vessel in Example 16.11. In that example, the dimensions of the vessel are given as the inside diameter, D = 6.5 ft, and tangent-to-tangent length, Z, = 40 ft. These dimensions are not... 

Unconstrained optimization (nonlinear programming), 2546-2553 classictil methods, 2546-2547 conjugate gradient methods, 2552-2553 golden section method, 2547-2549 line search techniques for, 2547 multidimensional search techniques for, 2549-2552... 

When the NLP problem consists of only one decision variable (or can be reduced to one), with lower and upper bounds, the optimal solution can be found readily with a spreadsheet, or by one of several structured and efficient search methods, including region elimination, derivative based, and point estimation, as described in detail by Reklaitis et al. (1983). Of the search methods, the golden-section method (involving region elimination) is reasonably efficient, reliable, easily implemented, and widely used. Therefore, it is described and illustrated by example here. 

II. 12-6.88 = 4.24 far from t. Whatever the best point, the final interval of uncertainty after four points is 4.24, vhereas the Fibonacci method yields a final range equal to 4 (or less with a value of d < 1). Nevertheless, if the search is stopped at the third point, the interval of uncertainty is 6.88 for the golden section and 7 for the Fibonacci method, which is only optimized for four points and a value of d = 1. 

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