TY - GEN A1 - Frese, Tobias A1 - Geiger, Ingmar A1 - Dost, Florian T1 - An empirical investigation of determinants of effectual and causal decision logics in online and high-tech start-up firms T2 - Small Business Economics Y1 - 2020 U6 - https://doi.org/10.1007/s11187-019-00147-8 SN - 1573-0913 VL - 54 IS - 3 SP - 641 EP - 664 ER - TY - GEN A1 - Geiger, Tobias A1 - Wachsmuth, Daniel A1 - Wachsmuth, Gerd T1 - Optimal control of ODEs with state suprema T2 - Mathematical Control and Related Fields N2 - We consider the optimal control of a differential equation that involves the suprema of the state over some part of the history. In many applications, this non-smooth functional dependence is crucial for the successful modeling of real-world phenomena. We prove the existence of solutions and show that related problems may not possess optimal controls. Due to the non-smoothness in the state equation, we cannot obtain optimality conditions via standard theory. Therefore, we regularize the problem via a LogIntExp functional which generalizes the well-known LogSumExp. By passing to the limit with the regularization, we obtain an optimality system for the original problem. The theory is illustrated by some numerical experiments. KW - Functional differential equations KW - differential equations with state suprema KW - optimality conditions KW - maximum principle KW - LogIntExp Y1 - 2021 U6 - https://doi.org/10.3934/mcrf.2021012 SN - 2156-8472 SN - 2156-8499 VL - 11 IS - 3 SP - 555 EP - 578 ER -