# History of Viennese Workshops

This is the 12th workshop in a series of events which started 31 years ago.

The preceding eleven workshops took place with a more or less three years recurrence time.

The 1st was organized in October 1981. The core topic was the dynamic theory of the firm by means of optimal control theory. The contributions of prominent researchers as A.Bensoussan, N.V.Long, S.Jorgenson and G.L.Thompson illustrate this approach (see Feichtinger, 1982).

The 2nd Viennese Workshop took place in 1984. Since then the spring-date (May, June) was kept. The number of papers presented as well as those of the participants increased substantially, as is illustrated by the second proceedings volume published again by North-Holland (Feichtinger, 1985). Specialists in optimal control theory and differential games, as T.Basar, R.F.Hartl, G.Leitmann, P.Michel, S.P.Sethi, and K.Sydsaeter presented interesting papers. A highlight was E.Dockner´s stability analysis for two-state optimal control models.

Another three years later the 3rd workshop was organized (see Feichtinger, 1988). Among the new contributors were F.Colonius, K.Nishimura and G.Sorger. The main issues of this workshop were persistent stable limit cycles as optimal solutions of economic models.

The 4th workshop took place in 1991. The reason for the one-year delay was that in 1990 a large Central European Operations Research conference was organized in Vienna by the Austrian OR-society jointly with the Swiss and German OR societies. The peer-referred papers were published in Feichtinger (1992). In particular, we refer those of M.Brokate, P.M.Kort, and F.Wirl.

In the nineties, bifurcations and chaotic behavior has become an important topic in dynamic economics. The 5th Viennese Workshop (which was shifted for one day to Bratislava) reflected this growing importance of nonlinear dynamical systems in economic analysis. Among the pertinent contributions let us mention that of C.H.Hommes, T.Mitra, L.Montrucchio, and A.Venditti. A selection of the papers presented was published in Dockner et al. (1998).

The 6th Viennese Workshop was organized in 1997. Optimal control models and differential games applications were published in the Annals of Operations Research (Dawid et al., 1999a). For contributions on nonlinear dynamical systems and adaptive methods compare Dawid et al. (1999b). Among the participants were C.Deissenberg, F.Gozzi, and R.Neck.

The 7th Workshop was held in May 2000. Among the contributors were C.Chiarella, W.Semmler, and J.Hofbauer. Some interesting papers on differential games presented at the meeting were published in Feichtinger et al. (2002). For other economic applications of nonlinear dynamical systems see Dawid et al. (2002). An additional outlet was a special issue of OCAM on optimal control applications (Feichtinger et al., 2001). Moreover, three of the papers presented at this workshop were published in the Essays in Honor of G.Feichtinger, edited by Dockner et al. (2000).

The 8th Workshop was held in 2003. Special attention was paid to multiple equilibria, Skiba points and age-structured (vintage) models using distributed parameter control. Plenary lectures were given by R.Day, E.J.Dockner , F.Clarke, F.Gozzi and H.Maurer.

The 9th Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics took place in May 2007 in Montreal, organized by Georges Zaccour. Among others, A.Haurie and G.J.Olsder presented two interesting papers.

Until now, the most recent Viennese Workshop was held in 2008 at the occasion of the retirement of G.Feichtinger. Only invited papers were presented by G.Leitmann, J.P.Caulkins, G.Sorger, H.Dawid, G.Zaccour, R.F.Hartl, P.M.Kort, F.O.O.Wagener, and E.J.Dockner.

After Bratislava and Montreal not surprisingly the 11th Workshop took place again outside of Vienna. Florian Wagener organized it in spring 2010 in Amsterdam. Important contributions werde made by B.LeBaron, W.Semmler and A.Xepapadeas.

A trade-mark of several of the Viennese Workshops was the presentation of optimal control applications for "unorthodox" situations, i.e. planning the "unusual" (compare also Feichtinger and Mehlmann, 1986). To illustrate those models we just mention

̶ aspects of optimal slidemanship,

̶ the economics of everything,

̶ optimal wine consumption,

̶ the Transsylvanian problem of renewable resources (vampirism), and

̶ the dynamics of extra-marital affairs.**References**

Dawid H., G.Feichtinger, R.F.Hartl (Eds., 2001): *Nonlinear Dynamics: Theory and Economic Applications*. Special Issue of *Central European Journal of Operations Research*** 9**, 1-2.

Dockner E.J., Feichtinger G., Sorger G. (Eds., 1998): *Journal of Economic Behavior and Organization* **33**, 3-4.

Dockner E.J., Hartl R.F., Luptacik M., Sorger G. (Eds., 2000): * Optimization, Dynamics, and Economic Analysis. Essays in Honor of Gustav Feichtinger*. Physica-Verlag Heidelberg.

Feichtinger G. (Ed., 1982): *Optimal Control Theory and Economic Analysis*. First Viennese Workshop on Economic Applications of Control Theory, Vienna, October 28 - 30, 1981, North-Holland, Amsterdam.

Feichtinger G. (Ed., 1985): *Optimal Control Theory and Economic Analysis 2*. Second Viennese Workshop on Economic Applications of Control Theory, Vienna, May 16 - 18, 1984, North-Holland, Amsterdam.

Feichtinger G. (Ed., 1988): *Optimal Control Theory and Economic Analysis 3*. Third Viennese Workshop on Optimal Control Theory and Economic Analysis, Vienna, May 20 - 22, 1987, North-Holland, Amsterdam.

Feichtinger G. (Ed., 1992): *Dynamic Economic Models and Optimal Control*. Fourth Viennese Workshop on Dynamic Economic Models and Optimal Control, Vienna, June 12-14, 1991, North-Holland, Amsterdam.

Feichtinger G., H.Dawid, R.F.Hartl (1999a): *Optimal Control and Differential Games. **Annals of Operations Research* **88**.

Feichtinger G., H.Dawid, R.F.Hartl (1999b): *Nonlinear Dynamical Systems and Adaptive Methods*. *Annals of Operations Research* **89**.

Feichtinger G., R.F.Hartl, P.Kort (Eds., 2001): *Economic Applications of Optimal Control*. Special Issue of *Optimal Control Applications and Methods*** 22,** 5/6.

Feichtinger G., Hartl R.F., Jorgensen S. (Eds., 2002): Special Issue on "*Economic Applications of Dynamic Games". International Game Theory Review*, Vol. **4**, Number 1 (March).

Feichtinger G., Mehlmann A. (1986): *Planning the unusual: applications of control theory to nonstandard problems. Acta Applicandae Mathematicae* **7**, 79-102.

Grass D., J.P.Caulkins, G.Feichtinger, G.Tragler, D.A.Behrens (2008): *Optimal Control of Nonlinear Processes. With Applications in Drugs, Corruption, and Terror*, Springer, Berlin.