Linear Programme 11
- Sciences
- 300 level
- 3 credit units
- 98 pages
- 4 units
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.
About this course
- Difficulty
- Intermediate
- Study hours
- 150 hours
- Maths
- Advanced
- Content
- Theoretical, problem solving
- Practical work
- No
- Assignments
- Tutor marked assignments
- Final examination
What you'll read
The real module and unit structure of FMT312, taken from the course material NOUN publishes.
One paragraph, so you can see how it reads
FMT312 · UNIT 1: BASIC CONCEPTS OF RN
The aim of the course is to bring to your cognizance the different methods of solving (Non-LPP) thus Non-Linear programming models in Finance as mentioned in the course content to handle Financial problems via the use of Statistics and calculations.
What you should be able to do
- Define continuous functions and differentiability in Rn
- Apply partial and directional derivatives
- Identify definiteness and semidefiniteness of quadratic forms
- Solve unconstrained optimization problems
- Solve constrained optimization problems using Lagrange multipliers
- Apply the Weierstrass theorem
What it prepares you for
- Financial Analyst
- Operations Research Analyst
- Data Scientist
- Statistician
- Economist
- Finance
- Economics
- Engineering
- Data Analysis
- Logistics
Where it gets hard
The units students slow down on, and what makes each one heavy.
- Module I: CLASSICAL OPTIMIZATION THEORY IN RN
Unit 1: Basic Concepts of Rn
Involves understanding and applying separation theorems, which require a solid grasp of real analysis concepts.
- Module II: Unconstrained Optimization
Unit 3: Unconstrained Optimization
Requires a strong understanding of gradients, Hessians, and their application in determining optimality conditions.
- Module II: Unconstrained Optimization
Unit 4: Constrained Optimization
Application of Lagrangian multipliers and understanding the conditions for optimality in the presence of constraints.
A suggested way through it
13 weeks, about 60 hours in total. Yours will differ.
- Week 1Module I: CLASSICAL OPTIMIZATION THEORY IN RN
Unit 1: Basic Concepts of Rn · 5 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 2Module I: CLASSICAL OPTIMIZATION THEORY IN RN
Unit 1: Basic Concepts of Rn · 5 hours
Solve problems involving quadratic forms and definiteness.. Practice identifying definiteness and semidefiniteness of matrices.. Study separation theorems, intermediate and mean value theorems..
- Week 3Module I: CLASSICAL OPTIMIZATION THEORY IN RN
Unit 2: Optimization in Rn · 5 hours
Define optimization problems in Rn.. Distinguish between constrained and unconstrained optimization problems.. Understand the objectives of optimization theory..
- Week 4Module I: CLASSICAL OPTIMIZATION THEORY IN RN
Unit 2: Optimization in Rn · 5 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 5Module II: Unconstrained Optimization
Unit 3: Unconstrained Optimization · 5 hours
Define local, global, and strict optima.. Apply first-order optimality conditions for unconstrained problems.. Practice finding gradients and Hessians..
- Week 6Module II: Unconstrained Optimization
Unit 3: Unconstrained Optimization · 5 hours
Apply second-order necessary and sufficient conditions.. Solve problems involving coercive functions and global minimizers.. Study convex sets and convex functions..
- Week 7Module II: Unconstrained Optimization
Unit 4: Constrained Optimization · 5 hours
Solve constrained optimization problems.. Apply Lagrangian techniques.. Practice problems with equality constraints..
- Week 8Module II: Unconstrained Optimization
Unit 4: Constrained Optimization · 5 hours
Apply first-order necessary conditions.. Apply second-order necessary and sufficient conditions.. Solve problems with inequality constraints..
- Week 9Module I: CLASSICAL OPTIMIZATION THEORY IN RN
Unit 1: Basic Concepts of Rn · 4 hours
Review Basic Concepts of Rn. Solve Tutor Marked Assignments.
- Week 10Module I: CLASSICAL OPTIMIZATION THEORY IN RN
Unit 2: Optimization in Rn · 4 hours
Review Optimization in Rn. Solve Tutor Marked Assignments.
- Week 11Module II: Unconstrained Optimization
Unit 3: Unconstrained Optimization · 4 hours
Review Unconstrained Optimization. Solve Tutor Marked Assignments.
- Week 12Module II: Unconstrained Optimization
Unit 4: Constrained Optimization · 4 hours
Review Constrained Optimization. Solve Tutor Marked Assignments.
- Week 13Module II: Unconstrained Optimization
Final Revision · 4 hours
Complete any pending assignments.. Prepare for final examinations..
Preparing for the exam
- Create concept maps linking Modules 1 and 2 core theorems.
- Practice unconstrained optimization problems from Unit 3 weekly.
- Review past TMAs, focusing on areas with lower scores.
- Dedicate extra time to Unit 4 Lagrangian techniques, solving diverse problems.
- Memorize key definitions and theorems from Units 1 and 2.
- Simulate exam conditions by solving practice problems within time limits.
Questions students ask about this course
What is FMT312 about?
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.
How many units does FMT312 have?
FMT312, Linear Programme 11, has 4 units across 1 module, over 98 pages of course material. You can read it one unit at a time.
How many credit units is FMT312?
FMT312 carries 3 credit units, at 300 level in Sciences.
Is FMT312 hard?
FMT312 is rated intermediate level, with advanced mathematical content. It is mostly theoretical and problem solving work.
How long does FMT312 take to study?
About 150 hours of study, spread across its 4 units.
How is FMT312 assessed?
FMT312 is assessed by assignments, tutor marked assignments and final examination.
What can I do with FMT312?
Financial Analyst, Operations Research Analyst, Data Scientist, Statistician and Economist.