COMPGV19  Numerical Optimisation
This database contains 201617 versions of the syllabuses. For current versions please see here.
Code  COMPGV19 

Year  MSc 
Prerequisites  None 
Term  2 
Taught By  Marta Betcke 
Aims  To provide the students with an overview of the optimization landscape and a practical understanding of most popular optimization techniques and an ability to apply these methods to problems they encounter in their studies e.g. MSc project/dissertation and later in their professional career. 
Learning Outcomes 

Content:
This module teaches a comprehensive range of state of the art numerical optimization techniques. It covers a number of approaches to unconstrained and constrained problems, methods for smooth and nonsmooth convex problems as well as basics of nonconvex optimisation.
This module is a core module in MSc in Scientific Computing.
Syllabus:
 Mathematical formulation and types of optimisation problems
 Unconstrained optimization theory e.g.: local minima, first and second order conditions
 Unconstrained optimization methods e.g.: linesearch, trust region, conjugate gradient, Newton, QuasiNewton, inexact Newton
 Smooth convex optimization: first order methods e.g. gradient descent, Nesterov, second order methods e.g. Newton
 Least Squares problems
 Constrained optimization theory e.g.: local and global solutions, first order optimality, second order optimality, constraints qualification, equality and inequality constraints, duality, KKT conditions
 Constrained optimization methods e.g.: linear programming, quadratic programming, penalty, barrier and augmented Lagrangian methods, least squares with smooth and nonsmooth regularization, nonlinear problems e.g. sequential quadratic programming
 Nonsmooth optimization e.g: subgradient calculus, subgradient methods, proximal ?operator, operator splitting, ADMM, nonsmooth penalties e.g. L1 or TV.?
Method of Instruction:
Weekly three hour lecture accompanied by a one hour practical tutorial, where the students get to implement (whenever practicable) and test performance of the methods taught in the lectures.
Assessment:
The course has the following assessment components:
 Coursework 1 (20%)
 Coursework 2 (20%)
 Project (60%)
Resources:
 Numerical Optimization, Jorge Nocedal and Stephen J. Wright, 2^{nd} edition, Springer
 PrimalDual InteriorPoint Methods, Stephen J. Wright, SIAM
 Convex Optimization, Stephen Boyd and Lieven Vandenberghe, Cambridge University Press