What does it mean to square a vector? Do you mean the square of its magnitude?
Suppose I have a "scalar" function which takes a "vector" ( ) for an argument:
The vector (D dimensional) takes only integer values.
Also suppose that , and are known.
To close the system we choose quasi-periodic boundaries .
I wish to find a "vector" such that takes its minimum value, under an assumption that , where the integer values of are known.
I'm looking for two kind's of solutions:
1) When I'm simply given a vector and asked to find , with some arbitrary initial guess for .
2) When I have found a solution to this problem, and then one of the 's is changed by 1.
Any advice on how to economically solve this problem would be greatly appreciated!
I seem to have left out the thing asked by Prove It:
This creature is not really a proper vector, and all calculations are done "element by element".
Following this, would mean the subtraction of L's ith element from the (i+1)th element, squared.
This subtraction is just the discrete version of the gradient of L at point i, where now L can be viewed as a discrete function.
Same goes for which must be true element by element.
Now that I think about it, this problem is a discrete form of finding the minimum of a function H depending on the function f(x) like:
With the condition: