chbe2120fall2010hw8

chbe2120fall2010hw8 - ChBE 2120 Homework 8 Due: Friday,...

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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 ൅2ݔݕെݕ 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 m-file 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 డ௫ ቀݔ డ௚ ܽቁ and ቀݕ ሺ௫ ,௬ 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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chbe2120fall2010hw8 - ChBE 2120 Homework 8 Due: Friday,...

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