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Linear Programming and AI Optimization Models VOL-1

Foundations Algorithms and Modern Applications in Operations Research and Machine Learning

This book is 100% completeLast updated on 2026-06-30

Unlock the power of optimization in the age of AI.

"Linear Programming and AI Optimization Models" delivers a masterful blend of classical Operations Research and modern Machine Learning applications. From the elegant Simplex Method to advanced decomposition techniques and KKT conditions, this Volume-1 builds a rock-solid foundation while demonstrating how these powerful algorithms .

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About the Book

"Linear Programming and AI Optimization Models: Foundations, Algorithms, and Modern Applications in Operations Research and Machine Learning (VOL-1)" is a comprehensive, self-contained guide that bridges classical optimization techniques with cutting-edge applications in Artificial Intelligence and Machine Learning.

This volume provides a rigorous yet accessible treatment of Linear Programming (LP), Integer Programming, and Nonlinear Programming, while highlighting their growing relevance in modern AI systems, operations research, supply chain optimization, logistics, resource allocation, and data-driven decision making.

Through clear explanations, detailed mathematical formulations, algorithmic walkthroughs, and real-world case studies, readers will master both the theoretical foundations and practical implementation of optimization models. The book emphasizes the synergy between traditional Operations Research (OR) methods and contemporary AI/ML techniques, making it an essential resource for professionals and academics navigating the intersection of these fields.

Key Features:

  • Progressive structure from foundational mathematics to advanced algorithms
  • Detailed coverage of the Simplex Method, duality, decomposition techniques, Branch-and-Bound, and KKT conditions
  • Rich collection of numerical examples, modeling exercises, and industry applications
  • Explicit connections between classical optimization and modern AI/ML models
  • Ideal for self-study, classroom use, and professional reference

Whether you are a student, researcher, data scientist, or operations professional, this book equips you with the tools to formulate, solve, and interpret complex optimization problems in today's AI-powered world.

Author

About the Author

Anshuman Mishra

Anshuman Kumar Mishra, M.Tech (Computer Science) Assistant Professor, Doranda College, Ranchi University

Prolific Author of 50+ Books on AI, Machine Learning & Computer Science | 20+ Years Experience

Anshuman Kumar Mishra is a dedicated educator, researcher, and highly prolific author with over 20 years of experience in Computer Science and Information Technology. Holding an M.Tech in Computer Science from BIT Mesra, he brings a rare combination of academic depth and practical teaching expertise.

Currently serving as Assistant Professor at Doranda College under Ranchi University, he has mentored thousands of students, helping them build strong foundations in programming, data science, and artificial intelligence. His student-centric teaching style emphasizes conceptual clarity, hands-on practice, and real-world application.

Anshuman is a prolific author with more than 50 books published across a wide spectrum of computer science and emerging technology domains. From foundational programming languages to advanced topics in Artificial Intelligence, Machine Learning, Reinforcement Learning, Decision Theory, and Computer Vision — his books are widely appreciated by students, educators, and professionals for their clear explanations, strong theoretical foundation, and practical approach.

His extensive body of work reflects his deep commitment to making complex subjects accessible and meaningful for learners at all levels. He is particularly recognized for creating well-structured learning paths that help readers progress from beginner to advanced levels with confidence.

Driven by the mission to democratize quality technical education, Anshuman continues to write and update books that bridge the gap between academic theory and industry practice.

When not teaching or writing, he actively follows and explores new developments in AI, Quantum Machine Learning, and Ethical Intelligence systems.

Contents

Table of Contents

Book Title “Linear Programming and AI Optimization Models: Foundations, Algorithms, and Modern Applications in Operations Research and Machine Learning VOL-1” Preface 1. Purpose of the Book VI-XI 2. Intended Audience 3. How to Use This Book 4. Prerequisites 5. Overview of Mathematical Notations ________________________________________ PART I: FOUNDATIONS OF OPTIMIZATION Chapter 1: Introduction to Optimization 1-36 1.1 What is Optimization? 1.2 Historical Evolution: LP to AI Optimization 1.3 Importance of Optimization in Modern ML & OR 1.4 Types of Optimization Problems 1.5 Applications in Academia, Industry, and Research ________________________________________ Chapter 2: Mathematical Preliminaries 37-70 2.1 Sets, Functions, and Relations 2.2 Vectors and Matrices 2.3 Convex Sets and Convex Functions 2.4 Calculus Essentials for Optimization 2.5 Norms, Distances, and Metrics ________________________________________ PART II: LINEAR PROGRAMMING (LP) Chapter 3: Formulation of Linear Programming Models 71-110 3.1 Decision Variables 3.2 Objective Function Types 3.3 Constraint Modeling 3.4 Standard and Canonical Forms 3.5 Feasible Region and Basic Feasible Solutions 3.6 Real-World LP Modelling Examples ________________________________________ Chapter 4: Simplex Method 111-142 4.1 Geometric Interpretation 4.2 Simplex Tableau 4.3 Pivot Operations 4.4 Optimality Conditions 4.5 Special Cases: Degeneracy, Unboundedness, Multiple Solutions 4.6 Numerical Examples ________________________________________ Chapter 5: Duality and Sensitivity Analysis 143-170 5.1 Primal and Dual Formulation 5.2 Dual Simplex Method 5.3 Complementary Slackness 5.4 Sensitivity Analysis 5.5 Shadow Prices and Economic Interpretation Chapter 6: Advanced Linear Programming Techniques 171-200 6.1 Revised Simplex Method 6.2 Benders Decomposition 6.3 Dantzig-Wolfe Decomposition 6.4 Cutting Plane Method 6.5 Transportation Models 6.6 Assignment Models 6.7 Network Flow Models ________________________________________ PART III: INTEGER & NONLINEAR PROGRAMMING Chapter 7: Integer & Mixed-Integer Linear Programming 201-231 7.1 ILP/MILP Formulation Techniques 7.2 Branch and Bound Method 7.3 Branch and Cut Method 7.4 Cutting Plane Methods for ILP 7.5 Scheduling and Routing Using MILP ________________________________________ Chapter 8: Nonlinear Programming 232-260 8.1 Convex vs Non-Convex NLP 8.2 Lagrange Multipliers 8.3 KKT Conditions 8.4 Quadratic Programming 8.5 Quadratically Constrained Programming 8.6 Nonlinear Optimization Applications

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