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Simulation

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Submitted By hemanand
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Steepest Descent Direction in Optimization - Application and Algorithm

Hemanand. T Department of Chemical Engineering,
St. Joseph’s College of Engineering,
Chennai – 600 119

Abstract: An analytical solution to identify the minimum value of a function used for optimization based on steepest descent technique was extensively discussed with applications in a process. The properties of gradient vector, the oscillation of function values and overshoot were analyzed in a function for the search of minimum. The best step size in each iteration was found by conducting a one-D optimization in the steepest descent direction. The five steps in the algorithm for steepest descent direction were done for the effective search for the minimum included (i) estimate of a starting design and set the iteration counter, (ii) selection of a convergence parameter, calculation of the gradient of function f(x) at the point, (iii) then stop the iteration process at the minimum point, otherwise, search for minimum by next iteration, (iv) calculation of step size to minimize and (v) updation of the design with the new values which yield minimization of an optimization process.

Keywords: Gradient Vector, Overshoot, One-D optimization, Convergence Parameter, Oscillation.

1. Introduction: In mathematics, optimization, or mathematical programming, refers to choosing the best element from some set of available alternatives. In the simplest case, this means solving problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. This (a scalar real valued objective function) is actually a small subset of this field which comprises a large area of applied mathematics. More generally, it means finding "best available" values of some objective function given a defined domain,

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