1 / 14

Introduction to Linear Optimization and Diet Problem Formulation

This lecture introduces the fundamentals of linear optimization, focusing on elementary linear programming concepts. Instructor Tsvetan Asamov discusses the diet problem as a practical application, emphasizing the need for constraints related to energy, protein, and calcium intake. Key topics include the formulation of the objective function, understanding feasible and optimal solutions, and exploring various types of linear programming problems such as unique optimal solutions, infeasible problems, and unbounded problems. Essential linear algebra concepts like vectors and matrices are also reviewed.

zarifa
Télécharger la présentation

Introduction to Linear Optimization and Diet Problem Formulation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Linear Optimization Lecture 1: Introduction Instructor: TsvetanAsamov

  2. Elementary Linear Programming with Applications, 2nd edition by Bernard Kolman and Robert E. Beck

  3. Example Need: Energy (2000 kcal), Protein (55 g), Calcium (800 mg)

  4. Example

  5. Diet Problem Formulation

  6. Linear Programming Examples

  7. Linear Programming • Objective function • Linear equations (equalities) • Linear inequalities • Linear equations and linear inequalities are referred to as linear constraints

  8. Standard Form

  9. Diet Problem • Objective function • Feasible solution • Optimal solution • Optimal value: 92.5

  10. Linear programming problems • Unique optimal solution • Many optimal solutions • No optimal solutions • Infeasible problems

  11. Linear programming problems • Unique optimal solution • Many optimal solutions • No optimal solutions • Infeasible problems • Unbounded problems

  12. Problems

  13. Problems

  14. Reading Assignment • Review linear algebra • Vectors • Matrices • Matrix multiplication • Matrix inversion • Gauss-Jordan reduction • Linear independence and basis • Subspaces

More Related