# Singapore University of Social Sciences

## Nonlinear Optimisation Methods and Applications (MTH309)

Applications Open: To be confirmed

Applications Close: To be confirmed

Next Available Intake: To be confirmed

Language: English

Duration: 6 months

Fees: To be confirmed

Area of Interest: Science & Technology

Schemes: Lifelong Learning Credit (L2C)

Funding: To be confirmed

### Synopsis

Optimization models are considered that are represented by constrained and unconstrained nonlinear functions. The various numerical solution techniques widely used to solve the nonlinear optimization models are covered. The computer software accompanying this course is used as a powerful tool to solve various nonlinear optmimization models.

Level: 3
Credit Units: 5
Presentation Pattern: Every January
E-Learning: BLENDED - Learning is done MAINLY online using interactive study materials in Canvas. Students receive guidance and support from online instructors via discussion forums and emails. This is supplemented with SOME face-to-face sessions. If the course has an exam component, This will be administered on-campus.

### Topics

• Nonlinear optimisation models.
• Iterative solution techniques.
• Induced instability.
• Ill-conditioning of optimisation models.
• Systems of non-linear equations.
• Nonlinear modelling problems.
• Minimisation of nonlinear functions.
• Minimisation of nonlinear functions of many variables.
• Unconstrained nonlinear optimisation.
• Rank, BFGS and Fletcher- Reeves methods.
• Constrained nonlinear optimisation.
• Lagrangian and Karush-Kuhn-Tucker (KKT) methods.

### Learning Outcome

• Apply the iterative solution techniques for nonlinear equations resulting from optimisation problems.
• Analyze the solution stability of nonlinear equations when model parameters are subject to small changes.
• Solve systems of nonlinear sets of equations with various numerical techniques.
• Use non-gradient search techniques to minimize unconstrained optimization models.
• Calculate the optimum of a nonlinear optimisation model with gradient search techniques.
• Demonstrate various solution techniques to minimize a constrained optimization model with equality and inequality constraints.
• Construct a range of mathematical techniques to solve a variety of quantitative problems
• Formulate solutions to problems individually and/or as part of a group.
• Analyze and solve a number of problem sets within strict deadlines.
• Verify solutions related to nonlinear optimization using Mathcad.