It is emphasized that mathematical programming methods are used to find the best solutions during the design process and for any problems that might come up. Design variables, objective functions, and constraints are used to set up issues related to optimization. Thus, the essential mathematical basis for approaching and solving optimization problems in various technical fields is outlined. The study of this subject is important because it is related to the optimization procedure and includes the utilization of algorithms, the establishment of optimization criteria, the exploration of potential integrations among various optimization methods, the investigation of potential integrations through iterative optimization methods, and the implementation of dimensional optimization. This study specifically examines the cylinder head of a conventional thermal engine. For this purpose, the Kuhn-Tucker conditions were used, which extend the method of Lagrange multipliers to include inequality constraints in optimization problems. The method proposed by the authors takes into account optimization criteria such as rigidity, mechanical and thermal resistance, uniform temperature distribution, and mass reduction. Through thermo-elastic and thermal analysis, the need for a configuration and dimensions that minimizes external surfaces of heat transfer to the external environment contributes to achieving the highest possible engine efficiency.