Optimisation

Course aim

Introduce students to basic concepts and methodologies for solving differentiable optimization problems, provide tools for them to produce a model, analyse it mathematically, and write a computer code that actually solves the model using standard (MATLAB) and cutting edge (CVX) computer software.

Course content

Preliminary concepts and definitions from Linear Algebra, Analysis and topology, Optimality conditions for Unconstrained Optimization: Global and local optima, first order optimality conditions, second order optimality conditions. Conditions for existence of solutions. The quadratic case. Least squares problem. The gradient method, scaled gradient method, Gauss-Newton Method. Convergence analysis of gradient methods. Newton's method, damped Newton method. Hybrid Gradient-Newton. Convex sets and its topological properties. Convex functions. Continuity and differentiability of Convex functions. Convex optimisation: Linear programming, convex quadratic problems. Examples of use of CVX software. Optimality for continuously differentiable problems over a convex constraint set. The KKT conditions. Application of KKT conditions: Constrained Least squares. Second order optimality conditions for inequality constrained problems.

Textbook(s)

Beck, Amir 2014, Introduction to Nonlinear Optimization, MOS-SIAM Series on Optimization

Prerequisite(s)

Corequisite(s)

Nil

Teaching method

Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.

Assessment

Continuous assessment, Examination, Problem solving exercise

Fees

EFTSL*: 0.125
Commonwealth Supported program (Band 2)
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Fee-paying program for domestic and international students
International students and students undertaking this course as part of a postgraduate fee paying program must refer to the relevant program home page to determine the cost for undertaking this course.

Non-award enrolment
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* Equivalent Full Time Study Load. Please note: all EFTSL values are published and calculated at ten decimal places. Values are displayed to three decimal places for ease of interpretation.