Advances in Optimization and Linear Programming

Ivan Stanimirović, PhD, is currently Associate Professor at the Department of Computer Science, Faculty of Sciences and Mathematics at the University of Niš, Serbia. He was formerly with 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. Stanimirović was the chairman of a workshop held at the 13th Serbian Mathematical Congress, Vrnjaèka Banja, Serbia, in 2014.

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 Methods in 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