Overview

This topic includes: Formulation of optimisation problems (objective functions and constraints, existence of an optimum); Elements of convex analysis (convex sets and functions, separation theorems); Necessary and sufficient optimality conditions (including Karush-Kuhn-Tacker theorem and convex duality results);Linear programming and elements of game theory; Sensitivity and perturbation analysis, Steepest decent method, … For more content click the Read More button below.

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Tuition pattern

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Aims

This topic aims to provide:

  • An understanding of main concepts of convex analysis
  • An understanding of necessary and sufficient optimality conditions
  • An understanding of the role of duality in optimisation theory
  • An understanding of linear programming and some concepts of the game theory
  • An understanding of the a role the sensitivity analysis in optimisation problems
  • An introduction to numerical methods for optimisation problems

Learning outcomes

On completion of this topic you will be expected to be able to:
1.
Understand the main concepts of optimisation theory and some concepts of game theory
2.
Use Lagrange multipliers to solve nonlinear optimisation problems
3.
Write down and apply Karush-Kuhn-Tucker conditions for constrained nonlinear optimisation problems
4.
Understand the importance of convexity in nonlinear optimisation problems
5.
Understand and be able to apply numerical optimisation techniques

Assessments

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Requisites information

Pre-requisites:
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