Convergence of the BFGS Method for LC 1 Convex Constrained Optimization 1

This paper proposes a BFGS-SQP method for linearly constrained optimization where the objective function f is only required to have a Lipschitz gradient. The KKT system of the problem is equivalent to a system of nonsmooth equations F(v) = 0. At every step a quasi-Newton matrix is updated if kF(v k)k satisses a rule. This method converges globally and the rate of convergence is su-perlinear when f is twice strongly diierentiable at a solution of the optimization problem. No assumptions on the constraints are required. This generalizes classical convergence theory of the BFGS method which requires a twice continuous diieren-tiability assumption on the objective function. Applications to stochastic programs with recourse are discussed on a CM5 parallel computer. Abbreviated title : BFGS method for LC 1 optimization