Optimisation - An Introduction: Professor Coralia Cartis, University of Oxford

Explore optimization techniques in this comprehensive lecture by Professor Coralia Cartis from the University of Oxford. Delve into the fundamentals of optimization, including minimizers, derivatives, and quadratic functions. Learn about various methods such as linear convergence, exact line search, and quadratic steps. Understand key concepts like the Armijo condition, direction theorem, and gradient methods. Discover the applications of steepest descent and scaling steepest descent techniques. Gain insights into the complexity of nonconvex optimization problems, compressed sensing, and parameter estimation for climate modeling. Suitable for those interested in algorithm development, analysis, and implementation for various problem classes in optimization.

Introduction
Minimizers
Derivatives
Second Derivatives
Quadratic functions
Methods
Linear convergence
Exact line search
Quadratic steps
Armijo condition
Direction
Theorem
Gradient method
steepest descent
scaling steepest descent
line search