TAOP23 Optimization 2011

Study Guide@lith

Valid for year : 2011

TAOP23	Optimization, 6 ECTS credits. /Optimeringslära/ For: DPU ENV IMM M MEC
	Prel. scheduled hours: 54 Rec. self-study hours: 106
	Area of Education: Science Main field of studies: Mathematics, Applied Mathematics,
	Advancement level (G1, G2, A): G2
	Aim: Optimization deals with mathematical theory and methods aiming at analyzing and solving decision problems that arise in technology, economy, medicine, etc. The course gives a broad orientation of the field of optimization, with emphasis on basic theory and methods for continuous and discrete optimization problems in finite dimension, and it also gives some insight into its use for analyzing practical optimization problems. After the course, the student shall: be able to identify optimization problems and classify them according to their properties, into, for example, linear and nonlinear, or continuous and discrete, problems construct mathematical models of simple optimization problems be able to define and use basic concepts, such as, for example, local and global optimality, convexity, weak and strong duality, and valid inequalities have knowledge about and be able to apply basic theory for some common types of optimization problems, such as, for example, duality theory for linear optimization problems, and have knowledge about and be able to use optimality conditions, such as, for example, Bellman's equations, to determine the optimality of a given solution have knowledge about and be able to apply basic principles for solving some common types of optimization problems, such as, for example, branch-and-bound for discrete problems be able to use relaxations, and especially Lagrangian duality, to approximate optimization problems, and be able to estimate the optimal objective value through lower and upper bounds be able to use commonly available software for solving optimization problems of standard type have some knowledge of practical applications of optimization
	Prerequisites: (valid for students admitted to programmes within which the course is offered) Calculus and Linear Algebra. Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
	Supplementary courses: Large Scale Optimization and Supply Chain Optimization.
	Organisation: The lectures and excercises treat principles for model formulation and the theory of optimality. Further, they also give training in mathematical modelling and in the use of solution methods which are based on the theory. The laboratory excercises demonstrate how computers can be used in the practical work with optimization problems.
	Course contents: Fundamental concepts within optimization, such as mathematical modelling, optimality conditions, convexity, sensitivity analysis, duality, and Lagrangean relaxation. Basic theory and methods for linear and nonlinear optimization, and integer and network optimization.
	Course literature: Jan Lundgren, Mikael Rönnqvist och Peter Värbrand: Optimeringslära (Studentlitteratur 2008) ISBN: 9789144053141 M Henningsson, Jan Lundgren, Mikael Rönnqvist och Peter Värbrand: Optimeringslära - Övningsbok (Studentlitteratur 2008) ISBN: 9789144053127 Jan Lundgren, Mikael Rönnqvist och Peter Värbrand: Optimization (Studentlitteratur 2010) ISBN: 9789144053080 M Henningsson, Jan Lundgren, Mikael Rönnqvist och Peter Värbrand: Optimization - Exercises (Studentlitteratur 2010) ISBN: 9789144053103
	Examination:
	Written examination Laboration	5 ECTS 1 ECTS


Course language is English. Department offering the course: MAI. Director of Studies: Torbjörn Larsson Examiner: Oleg Burdakov Link to the course homepage at the department Course Syllabus in Swedish

Linköping Institute of Technology
Contact: TFK , val@tfk.liu.se Last updated: 11/05/2010