Introduction to linear optimization and extensions with MATLAB

Content: Linear Programming Introduction General Linear Programming Problems More Linear Programming Examples Exercises Computational Project Geometry of Linear Programming Introduction Geometry of the Feasible Set Extreme Points and Basic Feasible Solutions Resolution (Representation) Theorem Exercises The Simplex Method Introduction Simplex Method Development Generating an Initial Basic Feasible Solution (Two-Phase and Big M Methods) Degeneracy and Cycling Revised Simplex Method Complexity of the Simplex Method Simplex Method MATLAB Code Exercises Duality Theory Introduction Motivation for Duality Forming the Dual Problem for General Linear Programs Weak and Strong Duality Theory Complementary Slackness Duality and the Simplex Method Economic Interpretation of the Dual Sensitivity Analysis Exercises Dantzig-Wolfe Decomposition Introduction Decomposition for Block Angular Linear Programs Master Problem Reformulation Restricted Master Problem and the Revised Simplex Method Dantzig-Wolfe Decomposition Dantzig-Wolfe MATLAB Code Exercises Interior Point Methods Introduction Linear Programming Optimality Conditions Primal-Dual Interior Point Strategy The Predictor-Corrector Variant of the Primal-Dual Interior Point Method Primal-Dual Interior Point Method in MATLAB Exercises Quadratic Programming Introduction QP Model Structure QP Application: Financial Optimization Solving Quadratic Programs Using MATLAB Optimality Conditions for Quadratic Programming Exercises Linear Optimization under Uncertainty Introduction Stochastic Programming More Stochastic Programming Examples Robust Optimization Exercises A Linear Algebra Review Bibliography