multivariate optimization by newton method

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

[Walter Roberson]

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]

yes i missed ] at the end. you wrote it correctly in the answer. it is cost = c { whole equation ] in which c is also a cost which varied with x and y

Answer 1

[Walter Roberson]

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.

[tian]

i get the value using fminsearch but not sure how to write the code for hessian and gradient matrix for newton method