Advances in Optimization and Linear Programming

This new volume provides the information needed to understand the simplex method, the revised simplex method, dual simplex method, and more for solving linear programming problems.Following a logical order, the book first gives a mathematical model of the linear problem programming and describes the usual assumptions under which the problem is solved. It gives a brief description of classic algorithms for solving linear programming problems as well as some theoretical results. It goes on to explain the definitions and solutions of linear programming problems, outlining the simplest geometric methods and showing how they can be implemented. Practical examples are included along the way. The book concludes with a discussion of multi-criteria decision-making methods.Advances in Optimization and Linear Programming is a highly useful guide to linear programming for professors and students in optimization and linear programming.

1. Introduction 1.1 Multiobjective Optimization 1.2 Symbolic Transformations in Multi-Sector Optimization 1.3. Pareto Optimality Test 1.4 The Method of Weight Coefficients 1.5 Mathematical Model 1.6 Properties of a Set of Constraints 1.7 Geometrical Method 2. Simplex Method 2.1 Properties of Simplex Methods 2.2 The Algebraic Essence of the Simplex Method 2.3 The Term Tucker’s Tables and the Simplex Method for Basic Permissible Canonical Forms 2.4 Algorithm of Simplex Method 2.5 Determination of the Initial Basic Permissible Solution 2.6 Two-Phase Simplex Methods 2.7 BigM Method 2.8 Duality in Linear Programming 2.9 Dual Simplex Method 2.10 Elimination of Equations and Free Variables 2.11 Revised Simplex Method 2.12 Cycling Concept and Anti-Cyclic Rules 2.13 Complexity of Simplex Methods and Minty-Klee Polyhedra 3. Three Direct Methodsin Linear Programming 3.1 Basic Terms 3.2 Minimum Angle Method 3.3 Dependent Constraints and Application of Game Theory 3.4 Algorithms and Implementation Details 3.5 Direct Heuristic Algorithm with General Inverses

Ivan Stanimirovic, PhD, is currently Associate Professor at the Department of Computer Science, Faculty of Sciences and Mathematics at the University of Niš, Serbia. Hewas formerlywith the Faculty of Management at Megatrend University, Belgrade, as a lecturer. His work spans from multi-objective optimization methods to applications of generalized matrix inverses in areas such as image processing and restoration and computer graphics. His current research interests include computing generalized matrix inverses and their applications, applied multi-objective optimization and decision-making, as well as deep learning neural networks. Dr. Stanimirovic was the chairman of a workshop held at the 13th Serbian Mathematical Congress, Vrnjaèka Banja, Serbia, in 2014.