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FMT312Sciences3 Unitsintermediate

Linear Programme 11

This course introduces students to methods of solving Non-Linear Programming Problems (NLPP). It covers classical optimization theory in Rn, including basic concepts, optimization problems, and the Weierstrass theorem. Students will learn about unconstrained and constrained optimization, gradients, Hessians, and optimality conditions. The course also explores quadratic forms, definite and semidefinite matrices, separation theorems, and the inverse and implicit function theorems.

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150h
Study Time
13
Weeks
12h
Per Week
advanced
Math Level
Course Keywords
Non-linear programmingOptimizationQuadratic formsKuhn-Tucker methodsGradient methods

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level
Builds on foundational knowledge
65%
intermediate
∑
Math Level
Advanced Math
📖
Learning Type
Theoretical Focus

Course Topics

Key areas covered in this course

1

Classical Optimization Theory

2

Basic Concepts of Rn

3

Unconstrained Optimization

4

Constrained Optimization

5

Quadratic Forms

6

Definite and Semidefinite Matrices

Total Topics6 topics

Ready to Start

No specific requirements needed

This course is designed to be accessible to all students. You can start immediately without any prior knowledge or specific preparation.

Assessment Methods

How your progress will be evaluated (3 methods)

assignments

Comprehensive evaluation of course material understanding

Written Assessment

tutor-marked assignments

Comprehensive evaluation of course material understanding

Written Assessment

final examination

Comprehensive evaluation of course material understanding

Written Assessment

Career Opportunities

Explore the career paths this course opens up for you

Financial Analyst

Apply your skills in this growing field

Operations Research Analyst

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Data Scientist

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Statistician

Apply your skills in this growing field

Economist

Apply your skills in this growing field

Industry Applications

Real-world sectors where you can apply your knowledge

FinanceEconomicsEngineeringData AnalysisLogistics

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module I: CLASSICAL OPTIMIZATION THEORY IN RN

5h

Unit 1: Basic Concepts of Rn

5 study hours
  • •Review definitions of continuous functions, differentiability, and continuous differentiable functions in Rn.
  • •Practice applying the concepts of partial derivatives and directional derivatives.
  • •Work through examples of finding higher-order derivatives.
Week
2

Module I: CLASSICAL OPTIMIZATION THEORY IN RN

5h

Unit 1: Basic Concepts of Rn

5 study hours
  • •Solve problems involving quadratic forms and definiteness.
  • •Practice identifying definiteness and semidefiniteness of matrices.
  • •Study separation theorems, intermediate and mean value theorems.
Week
3

Module I: CLASSICAL OPTIMIZATION THEORY IN RN

5h

Unit 2: Optimization in Rn

5 study hours
  • •Define optimization problems in Rn.
  • •Distinguish between constrained and unconstrained optimization problems.
  • •Understand the objectives of optimization theory.
Week
4

Module I: CLASSICAL OPTIMIZATION THEORY IN RN

5h

Unit 2: Optimization in Rn

5 study hours
  • •Apply the Weierstrass theorem to determine the existence of solutions.
  • •Work through examples to understand the conditions for solution existence.
  • •Solve tutor marked assignments.
Week
5

Module II: Unconstrained Optimization

5h

Unit 3: Unconstrained Optimization

5 study hours
  • •Define local, global, and strict optima.
  • •Apply first-order optimality conditions for unconstrained problems.
  • •Practice finding gradients and Hessians.
Week
6

Module II: Unconstrained Optimization

5h

Unit 3: Unconstrained Optimization

5 study hours
  • •Apply second-order necessary and sufficient conditions.
  • •Solve problems involving coercive functions and global minimizers.
  • •Study convex sets and convex functions.
Week
7

Module II: Unconstrained Optimization

5h

Unit 4: Constrained Optimization

5 study hours
  • •Solve constrained optimization problems.
  • •Apply Lagrangian techniques.
  • •Practice problems with equality constraints.
Week
8

Module II: Unconstrained Optimization

5h

Unit 4: Constrained Optimization

5 study hours
  • •Apply first-order necessary conditions.
  • •Apply second-order necessary and sufficient conditions.
  • •Solve problems with inequality constraints.
Week
9

Module I: CLASSICAL OPTIMIZATION THEORY IN RN

4h

Unit 1: Basic Concepts of Rn

4 study hours
  • •Review Basic Concepts of Rn
  • •Solve Tutor Marked Assignments
Week
10

Module I: CLASSICAL OPTIMIZATION THEORY IN RN

4h

Unit 2: Optimization in Rn

4 study hours
  • •Review Optimization in Rn
  • •Solve Tutor Marked Assignments
Week
11

Module II: Unconstrained Optimization

4h

Unit 3: Unconstrained Optimization

4 study hours
  • •Review Unconstrained Optimization
  • •Solve Tutor Marked Assignments
Week
12

Module II: Unconstrained Optimization

4h

Unit 4: Constrained Optimization

4 study hours
  • •Review Constrained Optimization
  • •Solve Tutor Marked Assignments
Week
13

Module II: Unconstrained Optimization

4h

Final Revision

4 study hours
  • •Complete any pending assignments.
  • •Prepare for final examinations.

This study schedule is in beta and may not be accurate. Please use it as a guide and consult the course outline for the most accurate information.

Course PDF Material

Read the complete course material as provided by NOUN.

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Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Create concept maps linking Modules 1 and 2 core theorems.

2

Practice unconstrained optimization problems from Unit 3 weekly.

3

Review past TMAs, focusing on areas with lower scores.

4

Dedicate extra time to Unit 4 Lagrangian techniques, solving diverse problems.

5

Memorize key definitions and theorems from Units 1 and 2.

6

Simulate exam conditions by solving practice problems within time limits.

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