MTH355 Basic Mathematical Optimization SUSS Assignment Sample Singapore

MTH355 Basic Mathematical Optimization is the perfect course for anyone interested in diving into the world of optimization. Engaging topics relating to linear and quadratic equations, calculus-based minimization techniques, convex analysis, deterministic algorithms and dynamic programming are all on the syllabus. Learners will build a strong foundation of knowledge to help them make decisions that require mathematical optimization tools.

Additionally, this course will provide a comprehensive overview of fundamental concepts, models, principles and techniques which can be applied in many real-world scenarios. In summary, MTH355 is ideal for anyone looking to maximize their understanding of mathematical optimization!

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In this section, we will describe some assignment activities. These are:

Assignment Activity 1: Formulate linear optimization problems into mathematical and graphical linear models.

Linear optimization problems are an important tool for businesses and organizations, as they allow dynamic decision-making to ensure that objectives are met in a cost-efficient manner. By formulating such problems into mathematical and graphical linear models, it becomes much easier to analyze the situation at hand and find solutions that optimize resources for desired results.

Such models enable problem solvers to gain insight into how different variables interact with each other, which can be further applied to make better decisions. With advanced software available nowadays, this process has become more accessible to users of all levels of experience. Overall, powerful linear optimization tools provide the capability not just to optimize existing business opportunities but also to uncover new ones.

Assignment Activity 2: Solve linear optimization modeling problems using the simplex method.

Linear optimization modeling is an incredibly powerful tool for optimizing outcomes given a set of constraints. The simplex method provides a great way for practitioners to take advantage of this tool; by decomposing a linear problem into its basic elements, practitioners can easily identify the constraints and objectives necessary to solve for a given problem.

With the simplex method, the end result will be an optimal solution that maximizes or minimizes the objective function while taking all relevant constraints into account. Although various forms of linear programming exist, it is inarguably the simplest and most effective method when it comes to solving linear optimization problems.

Assignment Activity 3: Analyze linear optimization problems with the two-phase simplex solution technique.

Linear optimization problems are a type of mathematical model with various applications in economics, engineering, and more. To analyze these problems, the two-phase simplex solution technique can provide an efficient method of finding optimal solutions. This technique first finds an initial basic feasible solution (IBFS) by solving a set of m linear equations with n variables.

Then it systematically variates the elements of the IBFS over a series of iterative steps to build an objective function until an optimal solution is reached by satisfying all associated constraints. Although this technique may require long computation times on complex models since each iteration must be carried out individually, it is ultimately invaluable in determining profitable strategies and improving business decisions through accurate data analysis.

Assignment Activity 4: Apply the LU decomposition technique and the conditions of convergence for linear sets of equations.

The LU decomposition technique is a very useful tool for problem-solving related to linear sets of equations. It can be used to decompose a matrix into its upper and lower triangular components, allowing the solving of equations quickly and efficiently. Before using this technique, it is important to ensure that the matrix fulfills certain conditions of convergence: it must be well-conditioned, diagonally dominant, or have positive diagonal elements.

If these conditions are met, then LU decompositions can generally be calculated accurately and in much less time than other techniques like Gaussian elimination. With this in mind, applying the LU decomposition technique and verifying the satisfaction of its related convergence conditions can effectively expedite equation-solving processes.

Assignment Activity 5: Employ the branch and bound method to solve integer programming and 0-1 variable models.

The branch and bound method is a powerful tool for solving integer programming and 0-1 variable models. It begins by forming an upper and lower bound for a given problem before branching off into separate subproblems. By doing so, the branch and bound method can significantly reduce the amount of time spent on an optimization problem with binary constraints.

This is especially true when the problem has a large number of variables, which often makes exhaustive search inefficient or prohibitively expensive. In addition, it can also be used to solve complex problems that involve multiple objectives in a relatively short amount of time, while providing optimal solutions in many cases.

Assignment Activity 6: Compute the optimum solution of a large linear programming model.

Finding the optimum solution to a large linear programming model can be a complex task. It requires deriving a mathematical answer, which involves iterations and testing. Specialized software is commonly used to assist with this process, as it helps simplify the calculations by providing efficient analytical methods. A range of algorithms are available that are optimized for different tasks, so selecting the right one is essential for obtaining an accurate conclusion. By meticulously executing each step of the process, you can ensure that you arrive at the most beneficial solution for your desired outcome.