Optimization bites

Short posts exploring optimization and operations research.

  1. Introduction to Operations Research
    1. What is Operations Research?
  2. Linear Optimization
    1. What is Linear Optimization?
    2. Graphical Solution
    3. Theoretical Analysis
    4. Simplex Algorithm
      1. The Simplex Algorithm
      2. Simplex Initialization
      3. Numerical Examples
      4. Simplex Convergence
    5. Duality
      1. Introduction to Duality
      2. Dual Simplex Algorithm
      3. Post-Optimization
  3. Integer Linear Optimization
    1. Introduction to integer optimization
    2. Modelling
    3. Branch and Bound
    4. Cutting Planes
      1. Gomory's Fractional Cutting Plane
      2. Gomory's Mixed-Integer Cutting Plane
    5. Modeling Challenges
      1. Sudoku
      2. The $n$-Queens Problem
      3. Einstein's Riddle
      4. Map Coloring
      5. Crossing the Bridge
      6. Hidato
      7. Dominosa
      8. Thermometers
      9. Queens Dominating the Board
      10. Binary Sudoku
      11. Knight's Tour on the Chess Board
      12. Hashi
      13. Number Sums
      14. Sudoku Killer
      15. Kakuro
      16. Murdoku
      17. Tower of Hanoi
  4. Nonlinear Optimization without Constraints
    1. Derivative-free Algorithms
      1. Uniform Search Algorithm
      2. Dichotomous Search Algorithm
      3. Golden Section Method
  5. Nonlinear Optimization with Constraints
    1. KKT Conditions for Problems with Inequalities
    2. KKT Conditions in Linear Optimization