Mathematical Optimization and Application of Nonlinear Programming

This chapter deals with mathematical optimization, focusing on the special role of convex optimization and nonlinear optimization for solving optimization problems. Optimization problems are highly significant at proposals of technological processes as well as projecting engineering objects, their realization and during their operation. In term of surface treatment of metals the time of the process duration is one of the most important parameters that determine the efficiency of the entire process. If we manage to minimize the time needed to create the layer with requested thickness at setting functioning factors, economic profit can be maximized at securing requested quality. To solve optimization problem nonlinear programming in Matlab was used. Based on the DOE methodology according to the central composite design, the set of experiments containing 40 runs has been performed in order to identify and analyse factors affecting the process of electrolytic alkaline zinc plating at a current density of \(0.5 \left[\mathrm{A} \cdot {\mathrm{dm}}^{-2}\right]\). The influence of seven input factors on the final thickness of formed zinc layer has been investigated and the mathematical-statistical model predicting the thickness of the formed layer is presented in the chapter. In order to save time, as the possibility of increasing the efficiency of the technological process, nonlinear programming was used to optimize the zincing process and the process of anodic oxidation, both belong to the surface treatment processes. In this chapter, we discuss selected optimization methods and mathematical models.