Module Contents: This module discusses continuous optimization problems where either the objective function or constraint functions or both are nonlinear. It explains optimality conditions, that is, which conditions an optimal solution must satisfy. It introduces the most popular numerical methods such as line search methods, Newton’s method and quasi-Newton’s methods and conjugate gradient methods for solving unconstrained optimization problems, and penalty function method and sequential quadratic programming methods for solving constrained optimization problems. Further, it explores
the theoretical background behind these powerful optimization methods by looking into how a specific method was motivated, developed, implemented and applied.
Characters: This module considers nonlinear continuous optimisation problems. This differentiates it from linear programming where the objective and constaint functions are affine. The continuity means that the decision variable may take continuous values instead of discrete values as in integer
programming. The module does not discuss mathematical modelling of practical problems; instead it focuses on numerical methods for solving standard optimization models of practical problems