Abstract
The Steepest descent method and the Conjugate gradient method to minimize nonlinear functions have been studied in this work. Algorithms are presented and implemented in Matlab software for both methods. However, a comparison has been made between the Steepest descent method and the Conjugate gradient method. The obtained results in Matlab software has time and efficiency aspects. It is shown that the Conjugate gradient method needs fewer iterations and has more efficiency than the Steepest descent method. On the other hand, the Steepest descent method converges a function in less time than the Conjugate gradient method.
Highlights
Optimization presents an essential tool in decision theory and analysis of physical systems
By looking at table 5 of example 3, one can see the last iteration for the Conjugate gradient method is g14 = [9.9914 × 10−9, 9.3203 × 10−8 ]T and the last iteration of the Steepest descent method is g32 = [4.6409 × 10−6, −2.0057 × 10−6 ]T .The results obtained from the Conjugate gradient method have more accuracy than the Steepest descent method, according to gk values
We can conclude that the Conjugate gradient method is more accurate than the Steepest descent method
Summary
Optimization presents an essential tool in decision theory and analysis of physical systems. Optimization theory is a very developed area with its wide applications in science, engineering, business management, military and space technology, location science, statistics, portfolio analysis, and machine computations [1,2,3,4,5,6,7]. The Steepest descent method ( known as Cauchy’s or gradient method) is one of the earliest and most fundamental methods of unconstrained scalar optimization. The technique is fundamental from a theoretical viewpoint, by using a simple optimization algorithm, the method can find the local minimum of a function. Fliege and Svaiter[15] presented a Pareto descent method for multi-objective optimizations. Drummond and Svaiter present a Cauchy-like method to solve smooth
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