The field of inverse problems and optimization is witnessing significant developments, driven by the need for efficient and robust methods to solve complex problems. A key direction is the integration of non-smooth optimization techniques with automated model discovery, enabling the efficient minimization of non-smooth objective functions and the selection of suitable regularization parameters. Another area of focus is the development of adaptive reproducing kernel methods, which can automatically select the proper kernel and induce a data-adaptive RKHS, outperforming standard methods with preselected kernels. Iterated variants of existing methods, such as the Golub-Kahan-Tikhonov method, are also being explored to produce higher-quality approximate solutions. Furthermore, refinements to existing theories and formulas, such as the Sinc convolution, are being made to improve convergence rates and resolve open problems. Notable papers include: The work on non-smooth optimization for automated material model discovery, which proposes new algorithms for efficiently computing the entire regularization path. The development of automatic reproducing kernel and regularization methods, which consistently outperform standard ridge regression and Gaussian process methods. The iterated Golub-Kahan-Tikhonov method, which produces more accurate approximate solutions than standard methods. The refinement of the Sinc convolution theory, which improves the convergence rate and resolves open problems.