Note on a method of conjugate subgradients for minimizing nondifferentiable functions

Abstract

An algorithm is described for finding the minimum of any convex, not necessarily differentiable, function f of several variables. The algorithm yields a sequence of points tending to the solution of the problem, if any; it requires the calculation of f and one subgradient of f at designated points. Its rate of convergence is estimated for convex and also for twice differentiable convex functions. It is an extension of the method of conjugate gradients, and terminates when f is quadratic. © 1974 The Mathematical Programming Society.