The recent developments in the research area have seen significant advancements in both optimization techniques and numerical methods for complex problems. There is a notable trend towards the development of specialized software packages that offer efficient solutions to specific types of optimization problems, particularly those involving multivariate polynomial cost functions. These packages are designed to outperform general-purpose solvers in terms of both solution quality and computational efficiency. Additionally, there is a growing interest in the application of advanced numerical methods to model and simulate complex physical and chemical phenomena, such as photodegradation in art conservation and nonlinear boundary value problems in mathematical modeling. These methods often incorporate innovative approaches to ensure accuracy and reliability, including the use of non-local integral operators and recursive integration formulas for singular finite elements. The field is also witnessing the exploration of new numerical techniques, such as Virtual Element Methods, for solving optimal control problems on complex geometries, with a focus on achieving high-order accuracy and robustness. Overall, the research is moving towards more specialized and efficient tools for tackling intricate problems across various domains.