Overview
This topic introduces techniques and theory for performing both linear and non-linear optimisation. In the linear case, the focus is on the simplex method, including discussions about convex sets, duality, algorithm runtime and perturbation analysis. These concepts are also applied to integer linear programs, graphs and combinatorial optimisation problems. For … For more content click the Read More button below.
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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.
Apply numerical optimisation techniques
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Requisites information
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