The lecture presents theory and solution methods for optimization
problems in science and technology.
The theory covers, in particular, the necessary and sufficient
optimality conditions for linear and nonlinear optimization as well as
the duality relations.
There are presented classical methods for linear and nonlinear
programming as well as the general approaches to discrete
programming and stochastic optimization.
Sensitivity analysis of optimal solutions is discussed.
Computer implementations of the solution methods and their availability
in the software packages are considered.
Decisions under Risk
The lecture deals with decision making under risk and uncertainty.
The methodology and specific techniques for decision support under
risk are widely presented and discussed.
The classical techniques of decision analysis are covered but
the main stress is given on the multiple criteria based interactive
techniques of decision support.
The lecture is focused on the scenario models of uncertainty
which corresponds to the current trends in decision support.
The latter allows to relate the decision support methodologies
to the classical (deterministic) optimization approaches.