Optimisation & Control

 The quest for minimum cost, maximum efficiency, or optimal performance measured by some other criterion is everywhere. It’s human nature, of course, but also the driving imperative of Nature in general – to the point where researchers trying to understand the world can approach their work by asking: “What is Nature trying to optimise?”

For dynamical systems originating in fields as diverse as molecular physics, mechanical engineering, or the economy, the problem of designing active interventions to shape the time-varying state of the system belongs to the field of control theory. Building something that works at all is an achievement; designing inputs that are provably best possible is even more challenging. But now Nature’s question becomes ours: what are we trying to optimise? Different scalar-valued criteria can be attached to different aspects of system behaviour, measurement, and performance, leading to specialist fields of interest to this Group’s Core Faculty.

Core Faculty

The Optimisation and Control Group is composed of a few core UKAAM faculty who are actively involved in the UKAAM activities and supervise UKAAM students or postdoctoral fellows. Prospective students interested in a research project in Optimisation and Control in the UKAAM are encouraged to contact one or more of the core faculty as potential supervisors and let them know of their interests.

Uri AscherUri is a Professor of Computer Science and a former Director of the UKAAM (1993-98). The focus of his work is the investigation and promotion of novel, efficient and reliable methods in scientific computation, particularly for approximation problems involving differential equations with constraints. He has contributed to a wide variety of applications and has also written several textbooks on numerical analysis published by SIAM.
Yankai CaoYankai’s research focuses on the design and implementation of large-scale local and global optimization algorithms to solve problems that arise in diverse decision-making paradigms such as machine learning, stochastic optimization, optimal control, and complex networks. His algorithms combine mathematical techniques and emerging high-performance computing hardware (e.g., multi-core CPUs, GPUs, and computing clusters) to achieve computational scalability. His goal is also to make these developments accessible to academic and industrial users by implementing algorithms on easy-to-use and extensible software libraries.
Michael FriedlanderMichael’s research is primarily in developing numerical methods for large-scale optimisation. He is especially interested in issues of convergence analysis, robust software implementation, and applications in signal and imagine processing, and machine learning.
Bhushan GopaluniProf. Bhushan Gopaluni has been with the department of chemical and biological engineering since 2006. His primary research interests are in time series modeling and control.
Eldad HaberEldad is a Professor of Mathematics and of Earth and Ocean Sciences. His main field of interest is the development of computational methods for inverse problems with applications to geophysical and medical imaging. The field is interdisciplinary by nature and includes numerical discretisation of partial differential equations, numerical optimisation and robust statistics. Eldad is an NSERC Industrial Research Chair in Computational Geoscience.
Philip LoewenPhilip is a theoretician with a soft spot for numerics. He works in the calculus of variations, optimal control theory and nonsmooth analysis, and takes also an active interest in engineering applications.
Ian MitchellIan is interested in numerical methods and software for solving ordinary and partial differential equations in the areas of control, robotics and verification. For example, the Toolbox of Level Set Methods is a Matlab software package which can be used for dynamic implicit surfaces in graphics, animation and fluid simulations as well as the Hamilton-Jacobi equation in control and verification.
Anthony PeirceAnthony’s principal areas of research expertise are in the application of asymptotic and numerical analysis to industrial problems. Research topics have included optimal control of molecular motion, stability of reactive fronts propagating in layered porous media, analysis of the regularisation effect of microstructure on localisation phenomena in elasto-plastic models, and development of multipole expansion techniques for boundary integral models of large-scale fracture interactions. His most recent research efforts are focussing on the analysis of hydraulic fracture propagation, which is of considerable importance in the oil, gas, and mining industries. Anthony was an interim UKAAM Director from 1999 to 2000.

Optimal path planning in robotics: original obstacles (top), adaptive mesh (centre), adaptive mesh paths (bottom)

Recommended Courses

Students interested in Optimisation and Control research in the UKAAM are advised to take the following preliminary, specific and optional courses:

Preliminary and Foundational Courses

CPSC 302: Numerical Computation for Algebraic Problems
CPSC 303: Numerical Approximation and Discretization
MATH 340: Introduction to Linear Programming
MATH 401: Green’s Functions and Variational Methods
MATH 402: Calculus of Variations
MATH 403: Optimal Stabilization and Control of Dynamical Systems
MATH 405: Numerical Methods for Differential Equations
MATH 441: Mathematical Modeling: Discrete Optimization Problems
MATH 442: Optimization in Graphs and Networks

Specific Courses

CPSC 406: Computational Optimization
CPSC 546: Numerical Optimization
MATH 547: Optimal Control Theory

Further Options

MATH 523: Combinatorial Optimization
EOSC 550: Linear Inverse Theory
EOSC 555: Nonlinear Inverse Theory