multivariate optimization by newton method
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i want to minimize following function using following equation
cost = cost [ (x/y/(1-x)^2)^0.6+(1-(x/y)/(1-y)^2)^0.6+6/y^0.6
what is the quickest and easiest method to find gradient and hessian matrix? tried to solve using matlab function diff but it is like never ending process please help
2 个评论
Walter Roberson
2011-5-1
There seems to be something wrong with the expression. The "[" is unmatched, and there seems to be a missing operation as otherwise cost would not occur on both sides of the expression.
tian
2011-5-1
回答（1 个）
Walter Roberson
2011-5-1
If the expression is just
cost = (x/y/(1-x)^2)^0.6+(1-(x/y)/(1-y)^2)^0.6+6/y^0.6
and if we interpret the 0.6 exponents as 3/5 rather than as 6/10 (which would imply raising negative components to an even power, creating a positive number, and then taking the 10th positive root of that positive number), then:
There are no solutions for x < 0 or y < 0, and
For any given x, the first real value occurs at
y = (1/6)*(-8+108*x+12*(-12*x+81*x^2)^(1/2))^(1/3) + (2/3)/(-8+108*x+12*(-12*x+81*x^2)^(1/2))^(1/3) + 2/3
and the value at that (x,y) is the minimum real expression value for that x value, and
As x increases, the minimum expression value decreases, with a limit of 0 as x goes to infinity.
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