This is the first in a new series of contributed, refereed volumes devoted to research in optimization by Australasian researchers and their collaborators. These volumes are intended to have wide scope and include survey papers by established researchers providing up-to-date information on research directions. This volume contains survey papers on the Clarke subdifferential and differentiability in Banach spaces, algorithms for solving nonsmooth equations, and control parametrization schemes in optimal control. Other topics covered include convex optimization, generalized convexity in optimization, nonsmooth analysis, and algorithms using approximations of sub-differentials.