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Mathematical optimization is concerned with finding the best available value of an objective function through appropriately choosing controllable variables/designer parameters within a set of given constraints. A broad variety of problems arising from diverse applications including production optimization in manufacturing, crew scheduling and aircraft assignment for airlines, optimal production and distribution of electricity or portfolio management in finance, can be formulated as mathematical optimization problems. This module presents the mathematical concepts and algorithmic tools for modeling and solving practical optimization problems.
1. Linear programming (the simplex algorithm, manufacturing, multiperiod models)
2. Integer programming (Assignment problems, optimization problems on graphs, shortest path problems, branch & bound)
3. Duality (Lagrange dual, weak & strong duality)
4. Convex optimization (convex functions, optimality conditions, duality, quadratic optimization)
5. Non-convex optimization (local vs. global optimization, optimality conditions, convex relaxations, )
6. Nonlinear optimization algorithms (gradient descent methods, quasi-Newton methods, interior-point methods, sub-gradients)
7. Optimization under uncertainty (uncertainty modeling, robust optimization, )
The coding language will be Python in this module
1. Linear programming (the simplex algorithm, manufacturing, multiperiod models)
2. Integer programming (Assignment problems, optimization problems on graphs, shortest path problems, branch & bound)
3. Duality (Lagrange dual, weak & strong duality)
4. Convex optimization (convex functions, optimality conditions, duality, quadratic optimization)
5. Non-convex optimization (local vs. global optimization, optimality conditions, convex relaxations, )
6. Nonlinear optimization algorithms (gradient descent methods, quasi-Newton methods, interior-point methods, sub-gradients)
7. Optimization under uncertainty (uncertainty modeling, robust optimization, )
The coding language will be Python in this module
About this Module
Student Effort Hours:
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Requirements, Exclusions and Recommendations
Not applicable to this module.
Module Requisites and Incompatibles
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Assessment Strategy
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Carry forward of passed components
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| Terminal Exam |
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| Name | Role |
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| Ms Rui Cai | Tutor |
| Cliodhna Gartland | Tutor |