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Mathematics Final Year Topic: Primal–Dual Certificates and Sensitivity in Small Linear Programmes

This Mathematics final year project uses exact examples to connect feasible solutions, bounds and changes in model parameters.

Why choose this project topic?

A focused study of linear-programming duality gives you a specific question in mathematical optimisation. It uses exact examples to connect feasible solutions, bounds and changes in model parameters. The bounded comparison creates room to explain how your evidence supports an interpretation and where the method has limits.

How do primal and dual solutions certify optimality, and when do small parameter changes alter the active constraints?

Agree the apparatus or dataset, comparison range and feasible measurement schedule for linear-programming duality with your supervisor.

Proposed project objectives

  1. 01Define the materials, variables and comparison conditions for linear-programming duality.
  2. 02Formulate bounded examples with explicit sign conventions and derive their duals.
  3. 03Evaluate the measurements or model outputs in relation to this question: How do primal and dual solutions certify optimality, and when do small parameter changes alter the active constraints?

A suggested research approach

Formulate bounded examples with explicit sign conventions and derive their duals. Verify feasibility and complementary slackness, then examine parameter intervals before and after the current basis or active set changes. Agree the available resources and record uncertainty, deviations from the protocol and any observations that challenge the initial interpretation.

What you will need

  • Small linear programmes with exact coefficients
  • Duality and complementary-slackness references
  • Exact solution checks and parameter-variation calculations

Keep your project scope clear

A reported shadow price is conditional on a sensitivity range and cannot be extrapolated to arbitrary parameter changes.

Mathematics project chapter outline

Use this outline as a starting point. You can edit the chapter titles to match your department’s format during setup.

  1. Chapter 1Introduction
  2. Chapter 2Literature Review
  3. Chapter 3Theory and Methodology
  4. Chapter 4Results and Applications
  5. Chapter 5Summary, Conclusion and Recommendations

Turn this topic into your own final year project.

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