An Accelerated Method for Minimizing a Convex Function of Two Variables

The author considers the problem of minimizing a convex function of two variables without computing the derivatives or (in the nondifferentiable case) the subgradients of the function, and suggests two algorithms for doing this. Such algorithms could form an integral part of new methods for minimizing a convex function of many variables based on the solution of a two-dimensional minimization problem at each step (rather than on line-searches, as in most existing algorithms). This is a contribution to research on nonsmooth optimization currently underway in System and Decision Sciences Program Core