This volume contains, in part, a selection of papers presented at the sixth Australian Optimization Day Miniconference (Ballarat, 16 July 1999), and the Special Sessions on Nonlinear Dynamics and Optimization and Operations ReΒ search - Methods and Applications, which were held in Melbourne, July 11-15 1999 as a part of the Joint Meeting of the American Mathematical Society and Australian Mathematical Society. The editors have strived to present both conΒ tributed papers and survey style papers as a more interesting mix for readers. Some participants from the meetings mentioned above have responded to this approach by preparing survey and 'semi-survey' papers, based on presented lectures. Contributed paper, which contain new and interesting results, are also included. The fields of the presented papers are very large as demonstrated by the following selection of key words from selected papers in this volume: β’ optimal control, stochastic optimal control, MATLAB, economic models, implicit constraints, Bellman principle, Markov process, decision-making under uncertainty, risk aversion, dynamic programming, optimal value function. β’ emergent computation, complexity, traveling salesman problem, signal estimation, neural networks, time congestion, teletraffic. β’ gap functions, nonsmooth variational inequalities, derivative-free algoΒ rithm, Newton's method. β’ auxiliary function, generalized penalty function, modified Lagrange funcΒ tion. β’ convexity, quasiconvexity, abstract convexity.