Digital Textbook

Optimization Techniques

Name: Optimization Techniques
Author: Prof. Mithun Mondal

From a single objective function to metaheuristic search — a complete, chapter-by-chapter course in formulating and solving optimization problems

Prof. Mithun Mondal EEE / ECE / EIE Undergraduate Course Free & Open Access

7Parts

30Chapters

3Method Families

Welcome

One optimization principle, built one chapter at a time

This is a living, web-native edition of a classic course in Optimization Techniques. Each of the 30 chapters lives on its own page — readable on any device, searchable, and free to share. The journey starts with how we translate a real engineering decision into a well-posed optimization problem and ends with the modern search algorithms that tackle problems too large or too rugged for classical methods.

The sequence follows the standard electrical, electronics, and instrumentation engineering syllabus, building from problem formulation and convexity through classical optimization and the KKT conditions, linear programming and the simplex method, duality and sensitivity, network and integer models, nonlinear programming, and finally metaheuristic and advanced optimization. Pick any chapter below to begin, or follow the seven parts in order for a complete first course.

How to use this book. Each part groups chapters by theme — first how a problem is modeled and when a solution is guaranteed to be optimal, then the workhorse of linear programming, its network and integer extensions, the tools of nonlinear programming, and finally the modern metaheuristics that search where gradients fail. The course spans three method families: classical analytical methods, mathematical programming, and nature-inspired search. Click a chapter card to open its dedicated page with concepts, equations, worked reasoning, and figures.

Part 1

Foundations of Optimization

Introduction · Problem Formulation · Convexity · Classical Methods · KKT Conditions

01Introduction to Optimization Techniques 02Formulating Optimization Problems 03Convex Sets and Convex Functions 04Classical Optimization: Unconstrained Problems 05Lagrange Multipliers and the KKT Conditions

Part 2

Linear Programming

Formulation · Graphical · Simplex · Big-M · Duality · Sensitivity

06Introduction to Linear Programming 07The Graphical Method 08The Simplex Method 09The Big-M and Two-Phase Methods 10Duality in Linear Programming 11Sensitivity and Post-Optimality Analysis

Part 3

Network and Transportation Models

Transportation · Assignment · Network Flows

12The Transportation Problem 13The Assignment Problem 14Network Optimization Models

Part 4

Integer and Dynamic Programming

Integer Programming · Branch & Bound · Cutting Planes · Dynamic Programming

15Integer Programming 16Branch and Bound and Cutting Plane Methods 17Dynamic Programming

Part 5

Nonlinear Programming

Line Search · Gradient Methods · Newton · Constrained NLP · Quadratic Programming

18One-Dimensional Search Methods 19Unconstrained Nonlinear Optimization 20Gradient-Based Methods 21Constrained Nonlinear Programming 22Quadratic and Geometric Programming

Part 6

Metaheuristic Optimization

Metaheuristics · Genetic Algorithms · PSO · ACO · Simulated Annealing · Tabu Search

23Introduction to Metaheuristics 24Genetic Algorithms 25Particle Swarm and Ant Colony Optimization 26Simulated Annealing and Tabu Search

Part 7

Advanced & Applied Optimization

Multi-Objective · Stochastic · Game Theory · Engineering Applications

27Multi-Objective Optimization 28Stochastic and Dynamic Optimization 29Game Theory and Decision Analysis 30Optimization in Engineering: Applications and Case Studies

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Start Here

Begin with Chapter 1 — Introduction to Optimization Techniques

Every optimization problem rests on one idea: choose the decision variables that make an objective as good as possible while respecting the constraints. The first chapter builds that foundation — objective functions, decision variables, constraints and the feasible region, local versus global optima, and the real-world engineering problems the entire course is built around. Open Chapter 1 →