Many decision problems arising in managerial decision making in the public as well as in the private sector are inherently nonlinear, and the same holds for various problems occurring in science and engineering. Tackling highly realistic nonlinear problems leads to solution methods totally different from those of, say, linear programming. In this course, the essential ideas as well as some of the most important solution algorithms for nonlinear decision problems are studied.

Most problems from management mathematics (discrete or continuous) are NP-hard. In other words, optimisation problems that arise in industry or in the public sector could not be solved exactly in reasonable computing time, even with modern computers. Therefore, when traditional mathematics techniques fail to give a fast answer, one should rely on near-optimal solution methods or heuristics. Ideas of classical heuristics (local search, hill climbing, greedy search, divide and conquer, A* search, dynamic programming etc.) will be studied first. A modern heuristics (metaheuristics) or general frameworks for building heuristics, usually gives rules of escaping from the so-called "local optima trap". Such methods are Tabu search, Simulated Annealing, Evolutionary Algorithms, Genetic Algorithms etc.

Learning Outcomes

By the end of the module students should be able to:

Understand and explain the basic concepts of nonlinear programming

Understand and explain first and second order optimality conditions

Understand and explain the role of convexity in optimisation

Explore this topic beyond the taught syllabus

Understand and explain why and when heuristic optimisation techniques are useful in Management Mathematics

Understand and explain the basic concepts of classical heuristic optimisation techniques

Design data structure for the computer code and apply rules of heuristics for that problem

Explore this topic beyond the taught syllabus

Assessment

33862-01 : Raw Module Mark : Coursework (100%)

Assessment Methods & Exceptions

2 hour Written Unseen January Examination (80%); In-course Assessment (20%).