Duality Course
Build expertise in linear programming duality starting from basics. Link linear algebra concepts, dual spaces, and shadow prices while solving primal-dual problems for practical planning and optimization. Perfect for mathematics experts seeking advanced insights and improved modeling abilities in higher dimensions.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This course offers a straightforward guide from setting up linear programs 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 optimization effectively.
Elevify advantages
Develop skills
- Model linear programs in matrix notation by identifying A, b, and c from constraints swiftly.
- Construct dual programs 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 programs and check strong duality plus slackness conditions.
- Apply duality theory to gain insights for production planning problems 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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