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Engineering Analysis ENG 3420 Fall 2009
Dan C. Marinescu
Office: HEC 439 B
Office hours: TuTh
11:0012:00
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Lecture 11
Lecture 11
±
Last time:
²
NewtonRaphson
²
The secant method
±
Today:
²
Optimization
±
Golden ratio
Æ
makes onedimensional optimization efficient.
±
Parabolic interpolation
Æ
locate the optimum of a singlevariable function.
±
fminbnd
function
Æ
determine the minimum of a onedimensional
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
Onedimensional versus multidimensional 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 onedimensional optimization efficient.
²
Parabolic interpolation
Æ
locate the optimum of a singlevariable function.
²
fminbnd
function
Æ
determine the minimum of a onedimensional 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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View Full Document 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 multidimensional optimization
±
Onedimensional 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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View Full Document 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 Multidimensional Optimization
±
Onedimensional 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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View Full Document 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.
 Spring '08
 Staff
 Neural Networks, Optimization

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