On the Extension of Constrained Optimization Algorithms from Differentiable to Nondifferentiable Problems

This paper presents three general schemes for extending differentiable optimization algorithms to nondifferentiable problems. It is shown that the Armijo gradient method, phase-I–phase-II methods of feasible directions and exact penalty function methods have conceptual analogs for problems with locally Lipschitz functions and implementable analogs for problems with semismooth functions. The exact penalty method has required the development of a new optimality condition.