Introduction to linear optimization and extensions with MATLAB
QA402.5 .K96 2014
- Unknown QA402.5 .K96 2014
- Includes bibliographical references (p. 329-335) and index.
- 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.
- (source: Nielsen Book Data)
- Publisher's Summary
- Filling the need for an introductory book on linear programming that discusses the important ways to mitigate parameter uncertainty, Introduction to Linear Optimization and Extensions with MATLAB(R) provides a concrete and intuitive yet rigorous introduction to modern linear optimization. In addition to fundamental topics, the book discusses current linear optimization technologies such as predictor-path following interior point methods for both linear and quadratic optimization as well as the inclusion of linear optimization of uncertainty i.e. stochastic programming with recourse and robust optimization. The author introduces both stochastic programming and robust optimization as frameworks to deal with parameter uncertainty. The author's unusual approach-developing these topics in an introductory book-highlights their importance. Since most applications require decisions to be made in the face of uncertainty, the early introduction of these topics facilitates decision making in real world environments. The author also includes applications and case studies from finance and supply chain management that involve the use of MATLAB. Even though there are several LP texts in the marketplace, most do not cover data uncertainty using stochastic programming and robust optimization techniques. Most emphasize the use of MS Excel, while this book uses MATLAB which is the primary tool of many engineers, including financial engineers. The book focuses on state-of-the-art methods for dealing with parameter uncertainty in linear programming, rigorously developing theory and methods. But more importantly, the author's meticulous attention to developing intuition before presenting theory makes the material come alive.
(source: Nielsen Book Data)
- Publication date
- Roy H. Kwon.
- Title Variation
- Linear optimization and extensions with MATLAB
- The operations research series