TY - GEN A1 - Benko, Matúš A1 - Mehlitz, Patrick T1 - Calmness and Calculus: Two Basic Patterns T2 - Set-Valued and Variational Analysis N2 - We establish two types of estimates for generalized derivatives of set-valued mappings which carry the essence of two basic patterns observed throughout the pile of calculus rules. These estimates also illustrate the role of the essential assumptions that accompany these two patters, namely calmness on the one hand and (fuzzy) inner calmness* on the other. Afterwards, we study the relationship between and sufficient conditions for the various notions of (inner) calmness. The aforementioned estimates are applied in order to recover several prominent calculus rules for tangents and normals as well as generalized derivatives of marginal functions and compositions as well as Cartesian products of set-valued mappings under mild conditions. We believe that our enhanced approach puts the overall generalized calculus into some other light. Some applications of our findings are presented which exemplary address necessary optimality conditions for minimax optimization problems as well as the calculus related to the recently introduced semismoothness* property. KW - Calculus KW - Calmness KW - Generalized differentiation KW - Inner calmness* KW - Set-valued analysis KW - Variation analysis Y1 - 2022 U6 - https://doi.org/10.1007/s11228-021-00589-x SN - 1877-0541 SN - 1877-0533 VL - 30 IS - 1 SP - 81 EP - 117 ER - TY - GEN A1 - Benko, Matúš A1 - Mehlitz, Patrick T1 - On the directional asymptotic approach in optimization theory Part A: approximate, M- , and mixed-order stationarity T2 - arXiv Y1 - 2022 UR - https://arxiv.org/abs/2204.13932 SP - 1 EP - 40 ER - TY - GEN A1 - Benko, Matúš A1 - Mehlitz, Patrick T1 - On the directional asymptotic approach in optimization theory Part B: constraint qualifications T2 - arXiv Y1 - 2022 UR - https://arxiv.org/abs/2205.00775 SP - 1 EP - 38 ER - TY - GEN A1 - Benko, Matúš A1 - Mehlitz, Patrick T1 - Why second-order sufficient conditions are, in a way, easy -- or -- revisiting calculus for second subderivatives T2 - arXiv Y1 - 2022 UR - https://arxiv.org/abs/2206.03918 SP - 1 EP - 43 ER -