Duality Course
Gain expertise in linear programming duality starting from basics. Link linear algebra, dual spaces, and shadow prices, then work through primal-dual problems for practical planning and optimisation. Perfect for mathematics experts seeking advanced insights and refined modelling abilities in higher dimensions.

from 4 to 360h flexible workload
certificate valid in your country
What will I learn?
This course provides a straightforward guide from setting up linear programmes to understanding their dual forms. Learners will represent problems using matrices, create primal-dual pairs, and link dual variables to shadow prices. With practical examples, you will tackle small problems, confirm strong duality and complementary slackness, and apply dual theory to real-world optimisation effectively.
Elevify advantages
Develop skills
- Model linear programmes in matrix notation by identifying A, b, and c from constraints swiftly.
- Construct dual programmes from primal ones using sign conventions and explain shadow prices clearly.
- Interpret dual spaces where matrix rows act as linear functionals and pricing mechanisms.
- Hand-solve compact primal-dual linear programmes and check strong duality plus slackness conditions.
- Apply duality concepts to production planning and optimisation scenarios in n-dimensional space.
Suggested summary
Before starting, you can change the chapters and workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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