Optimal Control Approach For Large

We propose an optimal control approach to tackle large scale unconstrained optimization problems. Our discussion begins with the introduction of a new framework to describe and deene the structure of a general function with a large number of variables. Based on the new concepts, a suucient condition is established so that any large scale unconstrained optimization problem satisfying this suucient condition can be solved in O(n) ops per iteration by optimal control algorithms which have local second-order convergence, where n is the number of variables. This optimal control approach could reduce the computational cost by a factor of n compared with the standard superlinear or quadratic optimization methods. Our application of this suucient condition on a collection of large scale un-constrained optimization problems in the literature indicates that the majority of these problems are amenable to this approach.