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The  [course_title] course combines optimisation theory and computation and teaches how you can use these two areas together for modern data analytics, economics, and engineering.

The course is split into four sections:

Firstly, the key concepts in linear algebra, calculus, and optimisation will be presented to you.

Secondly, you will be introduced with techniques of linear optimisation including basic polyhedral theory, simplex method, and duality theory.

Thirdly, the course focuses on convex conic optimisation while the last part deals with integer optimisation.


This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.


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Course Credit: Georgia Institute of Technology

Course Curriculum

Lesson 1
Introduction to Optimization 00:24:00
Mathematical Ingredients 00:11:00
Classification of Optimization Problems 00:10:00
A Portfolio Optimization Problem 00:10:00
Formulating a Portfolio Optimization Model 00:12:00
Solving the Portfolio Optimization Model 00:15:00
Summary of the Optimization Process 00:02:00
Lesson 2
Linear Algebra 00:16:00
Properties of Functions 00:02:00
Properties of Sets 00:10:00
Convex Functions 00:18:00
Convex Sets 00:02:00
Convex Optimization Problems 00:08:00
Lesson 3
Possible Outcomes 00:02:00
Local and Global Optimal Solutions 00:02:00
Idea of Improving Search 00:02:00
Optimality Certificates and Relaxations 00:24:00
Lagrangian Relaxation and Duality 00:02:00
Lesson 4
Lesson 1: Optimality Conditions L4 1 00:02:00
Lesson 2: Gradient Descent 00:11:00
Lesson 3: Newton’s Method 00:11:00
Methods for Univariat 00:07:00
Methods for Multivariate Function 00:08:00
Lesson 5
Introduction to LP Modeling 00:13:00
Optimal Transportation Problem 00:02:00
Maximum Flow Problem 00:02:00
Shortest Path Problem 00:11:00
How Electricity Markets Work 00:11:00
Modeling Power Plant Generating Using LP 00:10:00
Market Clearing Mechanism 00:14:00
A Real World Example 00:17:00
Lesson 6
Lesson 1: The Need to Make Decisions Under Uncertainty L6 1 00:12:00
Lesson 2: Two-Stage Stochastic Linear Programming 00:13:00
Lesson 3: Concrete Examples 00:12:00
Lesson 1: The Power of Piecewise Linear Functions 00:15:00
Lesson 2: Robust Regression Using LP 00:12:00
Lesson 3: Radiation Therapy 00:05:00
Lesson 4: LP Models for Radiation Therapy L6E 00:05:00
Lesson 7
Lesson 1: Basic Geometric Objects in LP L7 1 00:20:00
Lesson 2: Extreme Points and Convex Hull 00:02:00
Lesson 3: Extreme Rays and Conic Hull 00:13:00
Representation of Polyhedrons 00:13:00
Basic Feasible Solution 00:12:00
Polyhedron in Standard Form 00:02:00
Basic Solution in Standard Form LP 00:09:00
Basic Feasible Solution in Standard Form LP 00:02:00
Why Do We Care So Much About BFS? 00:11:00
Lesson 8
Local Search – The General Idea 00:11:00
Local Search – Specialized to LP 00:13:00
How to Walk on the Edge 00:13:00
When to Stop and Declare Victory 00:15:00
Summarize Simplex Method 00:09:00
Handling Degeneracy 00:17:00
Phase 1/Phase II Simplex Method 00:02:00
Lesson 4: Simplex Method Example 00:14:00
Lesson 9
Introduction to Duality Theory 00:10:00
Lagrangian Relaxation and LP Duality 00:21:00
Weak and Strong Duality 00:10:00
Table of Possibles and Impossibles 00:10:00
Complementarity Slackness 00:11:00
Concept of Robustness in Example 00:02:00
Robust Linear Program 00:02:00
More Examples of Robust Linear Program 00:10:00
Lesson 10
Cutting Stock Problem 00:09:00
Gilmore-Gomory Formulation 00:10:00
Column Generation 00:15:00
Column Generation for Cutting Stock Problem 00:02:00
Example for Column Generation 00:16:00
Primal-Dual Relationship: Constraint Generation 00:02:00
Primal-Dual Relationship: Pricing Problem and Separation Problem 00:10:00
Lesson 11
Exploiting Special Structures of Large-Scale Optimization 00:12:00
Dantzig-Wolfe Decomposition 00:10:00
Dantzig-Wolfe Decomposition 00:10:00
Example 00:14:00
Linear Equations, Norm, and Least Squares Problem 00:11:00
Function Fitting Using Least Squares 00:02:00
Normal Equation and Singular Value Decomposition 00:16:00
Convex Cones, Order, and Linear Conic Programming 00:12:00
Second-Order Cone and SOCP 00:02:00
PSD Cone and SDP 00:12:00
Experiment Design 00:02:00
Extremal Ellipsoid Problems 00:12:00
Lesson 12
Convex Cones, Order, and Linear Conic Programming 00:12:00
Second-Order Cone and SOCP 00:11:00
PSD Cone and SDP 00:12:00
Statistical Classification Problems 00:11:00
Experiment Design 00:18:00
Extremal Ellipsoid Problem 00:13:00
Lesson 13
Why Integer Variables 00:12:00
Discrete Optimization Challenges 00:02:00
Computational Complexity 00:17:00
Set Packing, Covering, Partition 00:10:00
Network Problems 00:02:00
Modeling Exercises – 1 00:12:00
Modeling Exercises – 2 00:12:00
Modeling Exercises – 3 00:04:00
Linear Programming Relaxation 00:07:00
Ideal Formulations 00:08:00
Branch-and-Bound Algorithm 00:08:00
An Example 00:06:00
Submit Your Assignment 00:00:00
Certification 00:00:00

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