Numerical Techniques for Stochastic Optimization

Rapid changes in todays environment emphasize the need for models and meth- ods capable of dealing with the uncertainty inherent in virtually all systems re- lated to economics, meteorology, demography, ecology, etc. Systems involving interactions between man, nature and technology are subject to disturbances which may be unlike anything which has been experienced in the past. In the technological revolution increases uncertainty-as each new stage particular, perturbs existing knowledge of structures, limitations and constraints. At the same time, many systems are often too complex to allow for precise measure- ment of the parameters or the state of the system. Uncertainty, nonstationarity, disequilibrium are pervasivE characteristics of most modern systems. In order to manage such situations (or to survive in such an environment) we must develop systems which can facilitate oar response to uncertainty and changing conditions. In our individual behavior we often follow guidelines that are conditioned by the need to be prepared for all (likely) eventualities: insur- ance, wearing seat-belts, savings versus investments, annual medical check.ups, even keeping an umbrella at the office, etc. One can identify two major types of mechanisms: the short term adaptive adjustments (defensive driving, mar- keting, inventory control, etc.) that are made after making some observations of the systems parameters, and the long term anticipative actions (engineer- ing design, policy setting, allocation of resources, investment strategies, etc.).