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| TAOP10 | Linear and Nonlinear Optimization, 4 p (sw) /Linjär och icke-linjär optimering M/ Advancement level: B | |
| Aim: The course gives basic knowledge in optimization methodology, with focus on the practical treatment of optimization problems with continuous variables. The course is intended to give the students (i) examples of areas within engineering design and production engineering where optimization methodology can be used (ii) practice in describing relevant parts of real-life systems using a mathematical model (iii) knowledge about the mathematical theory which leads to general optimality conditions (iv) examples of efficient methods that can be developed from this theory in order to solve practical optimization problemsPrerequisites: Calculus and Linear AlgebraSupplementary courses: TAOP25 Operations Research. TAOP34 Large Scale Optimization. TAOP 39 Applied Combinatorial OptimizationCourse organization: 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 content: Introduction: Optimization problems, examples of applications within engineering design and production engineering, Principles for problem formulation, linear and nonlinear models. Linear programming: Geometric interpretations, basic mathematical concepts, the simplex method, duality in linear programming, sensitivity analysis, applications in linear programming. Nonlinear programming: Nonlinear optimization problems without constraints, search methods, nonlinear problems with constraints, optimality conditions, the Karush-Kuhn-Tucker conditions, Lagrangean duality, Nonlinear applications in nonlinear programming. Course literature: A compendium. | ||
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