Optimization of a Water TankThis is a simple example of a geometric programming problem, involving the construction and operating costs of a cylindrical liquid (say, oil, or water) storage tank. The parameters are the diameter of the tank, and its height, . As seen here, the cost function of this problem is of the form where , , , and positive constants. The constraints involve upper and lower bounds on the variables: We might also have an upper bound on the aspect ratio of the tank (the aspect ratio constraint is useful to take into account structural resistance to wind): Our GP takes the standard form A CVX syntax for this problem is as follows. CVX syntax
cvx_begin gp variables h d % objective function is cost minimize( c1/(h*d^2) + c2*d^2 + c3*d*h ) subject to d <= dmax; h <= hmax; h/d <= alphamax; cvx_end See also: |