An Introduction To Optimization For Engineering Students

Write your own optimization codes for basic optimization problems in engineering and related fields.

What you'll learn

Basic Techniques in Engineering Optimization

Requirements

Basic calculus and linear algebra, computer programming skills.

Description

A basic introduction to optimization methods for engineering students which is often taught as part of an undergraduate-level engineering numerical methods class.  The material covered here is at that level, and includes one-dimensional optimization using Newton's and golden-search methods, multi-dimensional unconstrained optimization using direct and gradient methods, and constrained optimization using Lagrange multipliers.  Students should have basic computer programming skills using a language such as C, C++, Fortran90, MATLAB, or Python, and have a basic knowledge of multivariable calculus and linear algebra.  Course notes and codes (written in Fortran90) are available for download. 

Overview

Section 1: One-Dimensional Unconstrained Optimization

Lecture 1 Introductory Material

Lecture 2 Newton's Method for Root Finding

Lecture 3 Newton's Method for Optimization

Lecture 4 Secant Method for Optimization

Lecture 5 Example 1D Optimization Problem

Lecture 6 Golden Search Method

Lecture 7 Example Using Golden Search Method

Section 2: Multidimensional Unconstrained Optimization

Lecture 8 Brief Introduction

Lecture 9 Univariate Searches

Lecture 10 Gradient Methods Background Information

Lecture 11 Steepest Ascent Gradient Method

Lecture 12 Example Problem

Lecture 13 Computer Code to Solve Example Problem

Lecture 14 An Extension of Newton's Method to Multiple Dimensions

Section 3: Constrained Optimization Using Lagrange Multipliers

Lecture 15 Lagrange Multiplier Introductory Material

Lecture 16 Lagrange Multiplier Equality Constraint Example

Lecture 17 Computer Code and Problem Results

Lecture 18 Fixed-Point Iteration Solution of Lagrange Equations

Lecture 19 Fixed-Point Iteration Code

Lecture 20 Lagrange Multiplier Method for Inequality Constraints

Section 4: Applications

Lecture 21 Application 1

Lecture 22 Application 2

Lecture 23 Application 3

Lecture 24 Application 4

Lecture 25 Application 5

Engineering students at the sophomore/junior level and others interested in learning basic optimization techniques who have the necessary background.