In [S. Bütikofer, Math. Methods Oper. Res., 68 (2008), pp. 235–256] a nonsmooth Newton method globalized with the aid of a path search was developed in an abstract framework. We refine the convergence analysis given there and adapt this algorithm to certain finite dimensional optimization problems with $C^{1,1}$ data. Such problems arise, for example, in semi-infinite programming under a reduction approach without strict complementarity and in generalized Nash equilibrium models. Using results from parametric optimization and variational analysis, we work out in detail the concrete Newton schemes and the construction of a path for these applications and discuss a series of numerical results for semi-infinite and generalized semi-infinite optimization problems.
Studying a critical value function $\vi$ in parametric nonlinear programming, we recall conditions guaranteeing that $\vi$ is a $C^{1,1}$ function and derive second order Taylor expansion formulas including second-order terms in the form of certain generalized derivatives of $D \vi$. Several specializations and applications are discussed. These results are understood as supplements to the well--developed theory of first- and second-order directional differentiability of the optimal value function in parametric optimization.
This paper presents a dynamic model of talent investments in a team sports league with an infinite time horizon. We show that the clubs’ investment decisions and the effects of revenue sharing on competitive balance depend on the following three factors: (i) the cost function of talent investments, (ii) the clubs’ market sizes, and (iii) the initial endowments of talent stock. We analyze how these factors interact in the transition to the steady state as well as in the steady state itself.
This paper presents a model of a professional sports league and analyzes the effect of luxury taxes on competitive balance, club profits, and social welfare. It shows that a luxury tax increases aggregate salary payments in the league and produces a more balanced league. Moreover, a higher tax rate increases the profits of large-market clubs, whereas the profits of small-market clubs only increase if the tax rate is not set inadequately high. Finally, we show that social welfare increases with a luxury tax.
Wertschöpfungsnetzwerke leiden meist unter dem Dilemma, dass sie gleichzeitig effizient und innovativ sein müssen. Werden F&E- und Produktionsabteilungen organisatorisch aus diesem Grund getrennt, wird es schnell schwierig, diese Abteilungen zu koordinieren und den Wissenstransfer sicherzustellen. Leitfabriken können in bestimmten Konstellationen eine Vermittleroder Übersetzerrolle einnehmen und damit die Koordinationsprobleme lösen.
