ChBE 2120 Homework 8
Due: Friday, October 22, 2010 at 8:05 am
For most of this homework, you will maximize the following function (from homework 7):
max
݃
ሺݔ,ݕሻൌെ4ݔ
ଶ
2ݔݕെݕ
ଶ
ሺݔ,ݕ
డ
(1)
Solve the optimization problem above by the steepest ascent method, returning the values of x and y
that maximize the function as well as the function value at that point.
Save the mfile as a script
named
hw8_myGtAccountId.m.
The initial guess is
(x
0
,y
0
)
=(1.2,0.7).
Hints:

Before you start coding, it will be useful to compute the gradient
݃
ሻൌ
డ௫
డ
డ௬
by hand in
analytical form.
You should put this in a Matlab file called
hw8DelG_myGtAccountId.m
.
Try using a function declaration like:
function
outputVec = hw8delG_mstyczynski6(inputVec)
where inputVec would contain your x and y, while outputVec would contain your dfDx and
dfDy (this setup is useful for part 3).

Given what we did in class for steepest ascent optimization, to translate the function of two
variables above into a function of one variable, we would substitute all instances of x and y with
ሺ௫
,௬
ሻ
డ௫
ቀݔ
డ
ܽቁ
and
ቀݕ
ሺ௫
,௬
ሻ
డ௬
డ
ܽቁ
, respectively.
(This is the generalized form of the
specific examples we discussed in class.)
Put the resulting function into a Matlab function that
accepts as input a value for a, x
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 Spring '07
 Gallivan
 Calculus, Optimization, Newton Raphson, Golden Section, steepest ascent method

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