## MTM408 Optimization Methods

 Code MTM408 Name Optimization Methods Status Compulsory/Courses of Limited Choice Level and type Post-graduate Studies, Academic Field of study Mechanics, Mechanical Engineering, Machine Building Faculty Academic staff Jānis Vība, Jānis Auziņš, Olga Kononova Credit points 4.0 (6.0 ECTS) Parts 1 Annotation Extremes of analytic function. Extreme types. Minimum and maximum conditions of analytical function. General optimization problem formulation. Criteria and constraint types. Linear and nonlinear programming, the numerical methods. Gradient method. Local and global optimum. Universal and specialized optimization software. Functionals, the classical methods of functional minimization. Optimal control task standard form. Introduction to optimal control - Pontryagin maximum principle and dynamic programming. Introduction to multiobjective and robust optimization. In this course, students are not creating own optimization software codes, but will use specialized commercial software. Theoretical training target is to create the ability to formulate different optimization problems and use of commercial computer software for problem solution.. Goals and objectives of the course in terms of competences and skills To provide students with relevant information on the optimization task formulation and solving methods the following task should be fulfilled: identification of objective and constraints, the use of commercial software. The typical mechanical engineering optimization tasks are: machinery and mechanical statics and dynamics and control optimization. To achieve this aim, the following tasks are fulfilled: 1. The use of analytical methods for extreme search. 2. An overview of numerical optimization methods and their implementation in commercial software. 3. Many practical optimization problems of mechanics are solved during implementation of the training tasks: speed, strength, weight, cost, etc. optimization. 4. To understanding the complexity of optimization Learning outcomes and assessment Students will be able to apply analytical optimization methods to solve the simplest tasks. - Practical work/tasks Students will be proficient in the widely available optimization software. - Practical work/tasks Students will be able to formulate and solve nonlinear optimization tasks of the average complexity degree using the commercial software packages. - Questions in the coursework Students will be proficient in formulating/stating different optimization problems. - Exam Students will be able to choose the best method for the solution of linear, nonlinear, discrete and dynamic programming problems. - Exam Students will be able to assess the complexity and difficulty of different optimization task statements and solutions. - Exam Course prerequisites Mathematics. Mechanics. Physics.

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