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Optimization Theory

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.

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