NMAB02	Optimization, 15 ECTS-points /OPTIMERINGSLÄRA 1/ Advancement level: B
	Aim: The course is a basic course in optimization. It is organized in two parts, with emphasis on continuous and discrete variables, respectively. Both optimization theory and methodology are discussed. The course aims to give the students - a survey on important classes of optimization problems - ability in the analysis and in the mathematical modelling of technical and economical problems - knowledge about the construction of efficient methods and algorithms for solving optimization problems - ability in the solution of optimization problems, manually and with computer. Prerequisites: Participation in courses in the first year of the Master's degree program Mathematics, with at least 25 p and all labratory works. Supplementary courses: NMAD05 Large Scale Optimization NMAD06 Applied Combinatorial Optimization Course content: Part 1 (5p) with emphasis on optimization problems with continuous variables and with the items Convexity theory: Representation theorem, extreme points, basic solution, Fundamental theorem of linear programming, Farkas' lemma, separating hyperplane theorem, convex sets and functions, local and global optima, saddle point theorem, Karush-Kuhn-Tucker conditions, Lagrangean duality. Linear programming: Linear optimization models, graphic solution, the Simplex method, sensitivity analysis, duality. Nonlinear programming: nonlinear optimization models with and without constraints and solution methods for these problem types. Part 2 (5 p) with emphasis on optimization problems with discrete variables and with the items Integer programming: modelling, solution methods based on cutting plane, branch and bound and implicit enumeration, algorithms for specific integer problems, as knapsack problems, set covering and set partitioning problems. Network optimization: Problems with an underlying graph structure, linear programming with integrality property, transportation problem, shortest path problem, flows in networks. Dynamic programming: problems, modelling, methodology, optimality principle. Course literature: Bazaraa MS, Jarvis JJ, Sherali HD: Linear Programming and Network Flows, John Wiley & Sons 1990. Jönsson H, Migdalas S: Ickelinjär programmering, LiTH 1989. Holmberg K: Heltalsprogrammering och dynamisk programmering, LiTH 1989. Exempelsamling Optimeringslära I, del 1, LiTH 1999. Optimeringsproblem, LiTH 1993 Assessment:
TEN1	Written examination
TEN2	Written examination
LAB1
LAB2
	A written examination, written reports on computer exercises.

Course language is swedish.