Welcome to the Optimization Group in the CAAM Department. Our group currently consists of five CAAM faculty members whose research interests are maily focused on optimization. For most other CAAM faculty members, optimization is also an important methodology or tool in their research work.
A main mission of the Optimization Group in the CAAM department is to promote and coordinate research and educational activities in the areas of optimization.
Optimization is an active area in the field of computational and applied mathematics, focusing on providing best possible solutions to systems described by mathematical models. Nowadays, optimization techniques are widely used in areas of industrial operations, business and financial management, engineering design and control, oil reserve exploitation, data analysis, medical imaging and treatment, to mention just a few.
Optimization studies the mathematical problem of minimizing or maximizing a given objective function (a performance criterion) under a set of constraints or restrictions. For example, optimization is used to help make decisions in financial portfolio management where the objective is to maximize profit, while a constraint is to keep a certain measurement of investment risks below some given tolerable level.
The topics studied in optimization include optimality theory, problem formulations, development and analysis of computer algorithms, implementation and development of optimization-related computer software, and applications to various real-world problems. Optimization problems can be classified into continuous and discrete problems that generally require very different mathematical and computational approaches. However, interaction between the two branches has been increasing in recent years. The optimization group include both continuous and discrete optimizers (see the Faculty page for details).