Multivariable Constrained Optimization

[vaibhavphalak]

hi
i want to find values of a,b,c such that..

Minimize (a+b+c)
constrained to

(x-a)^2 + (y-b)^2 + (z-c)^2 less than equal to R(z)

(x-a)^2 + (y-b)^2 + (z-c)^2 greater than equal to r(z)

can anyone help me solving this?? which method should b used for better computation??

 

[vaibhavphalak]

in the above problem," x,y,z" are given and
one more constraint:

-z1 < z < z2

z1,z2 > 0.