MOSEK Modeling Cookbook

• 1 Preface
• 2 Linear optimization
  • 2.1 Introduction
  • 2.2 Linear modeling
  • 2.3 Infeasibility in linear optimization
  • 2.4 Duality in linear optimization
• 3 Conic quadratic optimization
  • 3.1 Cones
  • 3.2 Conic quadratic modeling
  • 3.3 Conic quadratic case studies
• 4 The power cones
  • 4.1 The power cone(s)
  • 4.2 Sets representable using the power cone
  • 4.3 Power cone case studies
• 5 Exponential cone optimization
  • 5.1 Exponential cone
  • 5.2 Modeling with the exponential cone
  • 5.3 Geometric programming
  • 5.4 Exponential cone case studies
• 6 Semidefinite optimization
  • 6.1 Introduction to semidefinite matrices
  • 6.2 Semidefinite modeling
  • 6.3 Semidefinite optimization case studies
• 7 Practical optimization
  • 7.1 Conic reformulations
  • 7.2 Avoiding ill-posed problems
  • 7.3 Scaling
  • 7.4 The huge and the tiny
  • 7.5 Semidefinite variables
  • 7.6 The quality of a solution
  • 7.7 Distance to a cone
• 8 Duality in conic optimization
  • 8.1 Dual cone
  • 8.2 Infeasibility in conic optimization
  • 8.3 Lagrangian and the dual problem
  • 8.4 Weak and strong duality
  • 8.5 Applications of conic duality
  • 8.6 Semidefinite duality and LMIs
• 9 Mixed integer optimization
  • 9.1 Integer modeling
  • 9.2 Mixed integer conic case studies
• 10 Quadratic optimization
  • 10.1 Quadratic objective
  • 10.2 Quadratically constrained optimization
  • 10.3 Example: Factor model
• 11 Bibliographic notes
• 12 Notation and definitions
• 13 References