Singapore University of Social Sciences

Applications Open: 01 May 2024

Applications Close: 15 June 2024

Next Available Intake: July 2024

Language: English

Duration: 6 months

Fees: \$1391.78 View More Details on Fees

Area of Interest: Science and Technology

Schemes: Alumni Continuing Education (ACE)

Funding: To be confirmed

School/Department: School of Science and Technology

Synopsis

MTH356 will provide undergraduates with an understanding of the common algorithms used in nonlinear optimisation. The topics covered are of central importance for many applications in data science and data analytics. The course gives a comprehensive introduction to the gradient method and that of constrained nonlinear programming. Additionally, the course covers how such algorithms are implemented using the software Baron. MTH356 will be paired with MTH355 so that students upon the completion of both courses receive a better comprehension of the contents in the specialist field of Optimisation.

Level: 3
Credit Units: 5
Presentation Pattern: EVERY JULY

Topics

• Basic Iterative Schemes to Solve Systems of Nonlinear Equations
• Convergence of Simple Iterative Methods of Nonlinear Equations
• Grid Search Method
• Golden Section Search
• Alternating Variable Search Method for a Minimum
• Steepest Descent Search Method for a Minimum
• Conjugate Direction Methods
• Stopping Criteria for the Iteration Methods
• Equality Constrained Models
• Newton-Lagrange Method
• Conversion to Equality Constraints
• Conditions for a Local Minimiser

Learning Outcome

• Solve single nonlinear equations and systems of nonlinear equations.
• Interpret the convexity of sets and functions.
• Determine the existence and uniqueness of solutions to a given nonlinear programming problem.
• Show the necessary and sufficient optimality conditions for a given nonlinear programming problem.
• Apply various numerical algorithms to solve nonlinear programming problems.
• Analyse the convergence of various gradient-based iterative methods.