# Lecture11 - Engineering Analysis ENG 3420 Fall 2009 Dan C....

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Engineering Analysis ENG 3420 Fall 2009 Dan C. Marinescu Office: HEC 439 B Office hours: Tu-Th 11:00-12:00

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2 Lecture 11 Lecture 11 ± Last time: ² Newton-Raphson ² The secant method ± Today: ² Optimization ± Golden ratio Æ makes one-dimensional optimization efficient. ± Parabolic interpolation Æ locate the optimum of a single-variable function. ± fminbnd function Æ determine the minimum of a one-dimensional function. ± fminsearch function Æ determine the minimum of a multidimensional function . ± Next Time ² Linear algebra
Optimization ± Critical for solving engineering and scientific problems. ² One-dimensional versus multi-dimensional optimization. ² Global versus local optima. ² A maximization problem can be solved with a minimizing algorithm. ± Optimization is a hard problem when the search space for the optimal solution is very large. Heuristics such as simulated annealing, genetic algorithms, neural networks. ± Algorithms ² Golden ratio Æ makes one-dimensional optimization efficient. ² Parabolic interpolation Æ locate the optimum of a single-variable function. ² fminbnd function Æ determine the minimum of a one-dimensional function. ² fminsearch function Æ determine the minimum of a multidimensional function. ± How to develop contours and surface plots to visualize two- dimensional functions. 3

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Optimization ± Find the most effective solution to a problem subject to a certain criteria. ± Find the maxima and/or minima of a function of one or more variables.
One- versus multi-dimensional optimization ± One-dimensional problems Æ involve functions that depend on a single dependent variable -for example, f ( x ). ± Multidimensional problems Æ involve functions that depend on two or more dependent variables - for example, f ( x , y )

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Global versus local optimization ± G lobal optimum Æ the very best solution. ± L ocal optimum Æ solution better than its immediate neighbors. Cases that include local optima are called multimodal . ± Generally we wish to find the global optimum.
One- versus Multi-dimensional Optimization ± One-dimensional problems Æ involve functions that depend on a single dependent variable -for example, f ( x ). ± Multidimensional problems Æ involve functions that depend on two or more dependent variables - for example, f ( x , y )

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Euclid’s golden number ± Given a segment of length the golden number is determined from the condition: The solution of the last equation is 2 1 y y 8 + 2 1 y y = ϕ 0 1 2 2 2 1 2 2 1 = + = ϕϕ y y y y y 680133 . 1 2 5 1 = + =
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## This note was uploaded on 02/17/2012 for the course EGN 3420 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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Lecture11 - Engineering Analysis ENG 3420 Fall 2009 Dan C....

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