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.

**Assessment**

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.

**Certification**

Edukite courses are free to study. To successfully complete a course you must submit all the assignment of the course as part of the assessment. Upon successful completion of a course, you can choose to make your achievement formal by obtaining your Certificate at a cost of £49.

Having an Official Edukite Certification is a great way to celebrate and share your success. You can:

- Add the certificate to your CV or resume and brighten up your career
- Show it to prove your success

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 | ||

Assessment | |||

Submit Your Assignment | 00:00:00 | ||

Certification | 00:00:00 |

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