Le doute n'est pas une condition agréable, mais la certitude est absurde.

Voltaire
...
Language: Persian
ISBN xxx-yyyy-zz-bbbbbb-t

Uncertain Optimization

Theory, Models, and Applications

In this book, various aspects of uncertainty in decision-making and mathematical models are investigated. The book is organized in four chapters. In the first chapter, the philosophy, concepts, and typology of uncertainty in mathematical programming have been discussed. The second part of the book is dedicated to stochastic programming methodology and its various methods. In the third chapter, robust optimization methods based on closed uncertainty sets are discussed. The fourth chapter of the book is dedicated to fuzzy mathematical programming methods and various robust fuzzy programming methods are investigated.

Extra Resources and Codes

  • Chapter Overview 1
  • Importance and Influence of Uncertainty
  • Philosophy of Uncertainty and Risk
  • Law of Noncontradiction and Uncertainty
  • Uncertainty Taxonomy
  • Uncertainty Methodologies in Mathematical Modelling
  • Robustness and Resiliency
  • Uncertainty Methodologies Taxonomy
  • Systematic Framework for Uncertainty Methodologies Taxonomy
  • Exercises

  • Chapter Overview
  • Probabilistic Prgramming with Costraints
  • Scenario-based Stochastic Programming
  • Realistic Robust Two-stage Scenario-based Programming
  • Worst-case Robust Two-stage Scenario-based Programming
  • Regret-based Robust Two-stage Scenario-based Programming
  • Mixed Chanced Scenario-based Approach
  • Multi-stage Scenario-based Approach
  • Scenario Generation Methods
  • Sample Average Approximation
  • Stochastic Value at Risk
  • Exercises

  • Chapter Overview
  • Robust Possibilistic Programming
  • Flexible Programming
  • Robust Flexible Programming
  • Uncertainty in Equality Constraints
  • Exercises