Knowledge-based economy has become a major trend in international society in the 21st century. However, today’s strategies place a greater emphasis on sustainability than in the past, while continuing to emphasize the importance of education and its connection with labour market. There has been a re-orientation, where resource, eco-efficiency and innovation have become major elements for achieving national objectives and a relevant level of competitiveness. This article deals with 30 indices, which define the competitiveness of a specific economy, and involve knowledge parameters. They are classified into four main categories and one special category. They are then analysed regarding the participation of Serbia and their availability. The main focus of this paper is to give detailed analyses of energy indices, as a special category of knowledge indexes. It has been shown that Serbia, in many cases, was not included in the study analysis or that there was insufficient information about Serbia’s position. This article shows that only a part of the presented indices includes Serbia. It is concluded that a new, revised model is needed that will include more exact indicators.

The paper shows an example of performed optimization of sizes in terms of welding costs in a characteristic loaded welded joint. Hence, in the first stage, the variables and constant parameters are defined, and mathematical shape of the optimization function is determined. The following stage of the procedure defines and places the most important constraint functions that limit the design of structures, that the technologist and the designer should take into account. Subsequently, a mathematical optimization model of the problem is derived, that is efficiently solved by a proposed method of geometric programming. Further, a mathematically based thorough optimization algorithm is developed of the proposed method, with a main set of equations defining the problem that are valid under certain conditions. Thus, the primary task of optimization is reduced to the dual task through a corresponding function, which is easier to solve than the primary task of the optimized objective function. The main reason for this is a derived set of linear equations. Apparently, a correlation is used between the optimal primary vector that minimizes the objective function and the dual vector that maximizes the dual function. The method is illustrated on a computational practical example with a different number of constraint functions. It is shown that for the case of a lower level of complexity, a solution is reached through an appropriate maximization of the dual function by mathematical analysis and differential calculus.