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.