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- Oliver Stein, Georg Still
- SIAM J. Control and Optimization
- 2003

We introduce a new numerical solution method for semi-infinite optimization problems with convex lower level problems. The method is based on a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized nonlinear complementarity problem functions. This approach leads to central path conditions for the lower level problems,… (More)

- Christodoulos A. Floudas, Oliver Stein
- SIAM Journal on Optimization
- 2007

- Oliver Stein, Georg Still
- European Journal of Operational Research
- 2002

The paper studies the connections and differences between bilevel problems (BL) and generalized semi-infinite problems (GSIP). Under natural assumptions (GSIP) can be seen as a special case of a (BL). We consider the so-called reduction approach for (BL) and (GSIP) leading to optimality conditions and Newtontype methods for solving the problems. We show by… (More)

- Oliver Stein
- Math. Program.
- 2012

- Oliver Stein
- Encyclopedia of Optimization
- 2004

This paper treats the solution of nonlinear optimization problems involving discrete decision variables, also known as generalized disjunctive programming (GDP) or mixed-integer nonlinear programming (MINLP) problems, that arise in process engineering. The key idea is to eliminate the discrete decision variables by adding a set of continuous variables and… (More)

- Oliver Stein
- European Journal of Operational Research
- 2012

After an introduction to main ideas of semi-infinite optimization, this article surveys recent developments in theory and numerical methods for standard and generalized semi-infinite optimization problems. Particular attention is paid to connections with mathematical programs with complementarity constraints, lower level Wolfe duality, semi-smooth… (More)

- Oliver Stein
- Math. Program.
- 2016

- Oliver Stein
- Optimization Letters
- 2016

- Hubertus Th. Jongen, Jan-J. Rückmann, Oliver Stein
- Universität Trier, Mathematik/Informatik…
- 1995

- Axel Dreves, Christian Kanzow, Oliver Stein
- J. Global Optimization
- 2012

Using a regularized Nikaido-Isoda function, we present a (nonsmooth) constrained optimization reformulation of a class of generalized Nash equilibrium problems (GNEPs). Further we give an unconstrained reformulation of a large subclass of all GNEPs which, in particular, includes the jointly convex GNEPs. Both approaches characterize all solutions of a GNEP… (More)