How to use quadprog for a function with time dependent constant?

I have an optimization problem where to goal is to minimize the following equation:

f(x) = aβx² - ax + ay + b

where a, b and β are constants and y is a vector of constants. x is the decision variable and is also a vector of the same length as y. To use quadprog to solve this problem, this has to be in the form

f(x) = 1/2 xᵀHx + fᵀx

How do I put my equation in that form when it has the constant in the form of a vector?

Thanks very much!

[Matt J]

It is not clear how your f(x) works out to be scalar-valued. If it is not scalar-valued, quadprog is not applicable and, in fact, it is fundamentally unclear what it means to "minimize" it.

Answer 1

[Matt J]

Don't bother. The minimizing x in your case is given trivially by

xmin=1./(2β)

and the minimum value is then f(1./(2β))