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. Many of these nonlinear optimization problems can be formulated as convex conic programming problems, with different choices of the cone. In this course, the essential ideas as well as the most important classes of conic programming, second-order and semidefinite, are studied in detail. Applications of conic programming, for instance in robust optimization and eigenvalue optimization are also studied.

Tackling highly realistic nonlinear problems leads to solution methods totally different from those of, say, linear programming. In this course, further theory as well as several highly innovative solution methods for nonlinear decision problems are studied. This module further develops knowledge of both constrained and unconstrained optimisation.

Learning Outcomes

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

Understand and explain basic concept of conic programming

Formulate optimisation problems as conic programs

Formulate dual problems to different conic problems

Understand and explain further concepts of nonlinear programming

Discuss several different solution methods, apply them, and understand their limitation in practice

Discuss recent trends and latest developments in nonlinear programming