This book focuses on selected methods of applied mathematics that are aimed at mathematical optimization, with an emphasis on their application in engineering practice. It delves into the current mathematical modeling of processes and systems, with a specific focus on the optimization modeling of technological processes. The authors discuss suitable linear, convex, and nonlinear optimization methods for solving problems in engineering practice. Real-world examples and data are used to numerically illustrate the implementation of these methods, utilizing the popular MATLAB software system and its extension to convex optimization. The book covers a wide range of topics, including mathematical modeling, linear programming, convex programming, and nonlinear programming, all with an engineering optimization perspective. It serves as a comprehensive guide for engineers, researchers, and students interested in the practical application of optimization methods in engineering.

Alena Vagaská, PhD, has 27 years of experience as pedagogue and scientist at the Technical University of KoSice, Faculty of Manufacturing Technologies, PreSov, Slovak Republic. Her research focuses on applied mathematics, statistics, optimization, engineering manufacturing (and multidisciplinary), material sciences (multidisciplinary) and education/educational research.

Miroslav Gombár, Ph.D, has over 25 years of experience in surface treatment engineering practice (in company aimed on surface treatment processes) and 15 years of experience in top management. He has been working as a teacher and scientist at several universities, such as Technical University in KoSice and the University of PreSov in PreSov. His research focuses in engineering manufacturing (and multidisciplinary), material sciences (multidisciplinary), mechanical engineering, business and management, applied mathematics, statistics, optimization and education/educational research.

Anton Panda, Ph.D, is an associate professor of manufacturing technologies, FMT TU KoSice. He has about 30 years of experience in the engineering company supplying the products for demanding automotive, also farm and agricultural industry (constructor of special purpose machinery and equipment, systems analyst, head the department of development and technical preparation of production, methodist of statistical methods, commercial and technical director, director of quality). Since 2008 (since 1994 external), he operates as a pedagogue and scientist at the Faculty of Manufacturing Technologies TU KoSice with the seat in PreSov, as well as an expert-coordinator (auditor) of quality management systems. He is recognized as an expert for the production of bearings in companies in Germany, Italy, China, Slovakia and Czech Republic. Since 2014, he is a member of the Polish Academy of Sciences. Since 2014, he is a member of the ASME, USA.

1. Optimization in Historical Context.- 2. Optimization.- 3. Optimization Methods in General.- 4. Selected Methods of Multidimensional Optimization.- 5. Optimization of Technological Processes.