Optimization Methods Application in Automation

Major: Automation and Computer-Integrated Technologies
Code of subject: 8.151.00.M.011
Credits: 3.00
Department: Automation and Computer-Integrated Technologies
Lecturer: Assistant Professor Dilai Ihor Volodimirovich
Semester: 2 семестр
Mode of study: денна
Learning outcomes: - knowledge of modern concepts, methods of research in the field of automation and computer-integrated technologies; - the ability to demonstrate in-depth knowledge in the selected field of scientific research; - to apply knowledge and understanding for solving the synthesis and analysis of automation systems, computer-integrated technologies and their elements; - to investigate and model phenomena and processes in complex dynamic systems for automatic management of organizational and technological processes; - evaluate the feasibility and possibility of using new methods and technologies in the tasks of synthesis of automatic control systems technological processes; - To argue the choice of methods for solving a scientific and applied task, critically evaluate the results and defend the decisions.
Required prior and related subjects: Prerequisites: Automatic control theory Numerical methods Computer-aided design automation Presentation of scientific research results
Summary of the subject: Introduction. Optimization tasks in the field of automation. Classic optimization methods. The essence of classic optimization methods. Necessary and sufficient conditions of the extrema of the function. Minimum, maximum and inflection points of functions. Local and global extremes. Software tools for solving Matlab and Maple optimization tasks. Maple programming environment. Maple Computer Algebra System Interface. Maple objects: expressions, numbers and constants, ribbons; kits and lists; functions for solving systems of linear and nonlinear equations, inequalities; arrays. Programming in the Maple environment. Matlab tools for solving optimization tasks. Optimization ToolBox. Methods of one-parameter optimization. Unimodal features. Dichotomy, Fibonacci Methods and the Golden Intersection and the Relationship Between Them. Quadratic and cubic approximation methods. Algorithms and software implementation in Matlab and Maple. Methods of multivariable optimization. Multivariable optimization criteria. Scalar field. Scalar field gradient, Hessian matrix. Necessary and sufficient conditions of extrema of function, saddle points, positive definiteness of Hessian matrix. Classic methods for optimizing the functions of many variables. Determining the extremum of functions of many variables. Heuristic methods of direct search for extremum. Method for coordinate descent. Simple method of finding the minimum of a function. The Nelder-Mid method. The method of conjugated directions. The essence of the conjugate method. Quadratic criteria. Powell's method. Algorithms and software implementation in Matlab and Maple. Gradient Search Methods. Nonlinear optimization with constraints. Classic methods of conditional optimization. The Lagrange multiplier method. Limitations are given by inequalities. The Kuhn-Tucker task. Nonlinear programming. The essence of methods for determining extrema in constrained problems. The method of penalty functions. Types of penalties in the form of equalities and inequalities. Principles of nonlinear programming. Algorithms and software implementation in Matlab and Maple. Basic iterative procedure for gradient search methods. Cauchy and Newton methods. The conjugate gradient method (Fletcher Reeves). The Quasi-Newtonian David-Fletcher-Powell method.
Assessment methods and criteria: - written reports on laboratory works, oral questioning (50%); - final control (control measure - exam): written and oral form (50%).
Recommended books: 1. Reclays G., Reyvindron A., Ragsdel K. Optimization in engineering. 1-1. - M .: Mir, 1986. 2. Bundy U.B. Optimization methods. Introductory course. - M .: Radio and communication, 1988. 3. Lesin VV, Lisovets Yu.P. Basics of optimization methods. - M .: MAI, 1998. 4. Panteleev AV, Letova TA Optimization methods in examples and tasks. - M .: Higher. , 2005. 5. Gill F., Murray U., Wright M. Practical optimization. - M .: Mir, 1985.