Advanced Mathematical Optimization

Singapore University of Social Sciences

Advanced Mathematical Optimization (MTH356)

Applications Open: 01 May 2023

Applications Close: 15 June 2023

Next Available Intake: July 2023

Course Types: Modular Undergraduate Course

Language: English

Duration: 6 months

Fees: $1378 View More Details on Fees

Area of Interest: Science and Technology

Schemes: Alumni Continuing Education (ACE), Lifelong Learning Credit (L2C)

Funding: To be confirmed

School/Department: School of Science and Technology

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Synopsis

MTH356 will provide undergraduates with an understanding of the common algorithms used in nonlinear optimization. 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. MTH356e will be paired with MTH355e so that students upon the completion of both courses receive a better comprehension of the contents in the specialist field of Optimization.

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.
Analyze the convergence of various gradient-based iterative methods.