Area-time complexity of the unconstrained minimization problem

The purpose of this paper is to investigate the complexity of unconstrained optimization, in VLSI models. The complexity results are stated in terms of the costumary AT^2 (area(time)^2) measure [6,7]. First, we note that the above problem is more general than matrix inversion or linear system solution. Then we present a design which provides an upper bound to the areax (time)^2 complexity of unconstrained minimization, in the case of quadratic functions, which is close to the known areax (time)^2 lower bounds to matrix inversion [5,6], up to logarithmic factors.