An Introduction To Optimization For Engineering Students

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.


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