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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)

- Marco A. López, Georg Still
- European Journal of Operational Research
- 2007

A semi-infinite programming problem is an optimization problem in which finitely many variables appear in infinitely many constraints. This model naturally arises in an abundant number of applications in different fields of mathematics, economics and engineering. The paper, which intends to make a compromise between an introduction and a survey, treats the… (More)

- 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)

- Georg Still
- European Journal of Operational Research
- 1999

Generalized semi-infinite optimization problems (GSIP) are considered. The difference between GSIP and standard semi-infinite problems (SIP) is illustrated by examples. By applying the ’Reduction Ansatz’, optimality conditions for GSIP are derived. Numerical methods for solving GSIP are considered in comparison with methods for SIP. From a theoretical and a… (More)

- Gemayqzel Bouza Allende, Georg Still
- Math. Program.
- 2013

Bilevel programs (BL) form a special class of optimization problems. They appear in many models in economics, game theory and mathematical physics. BL programs show a more complicated structure than standard finite problems. We study the so-called KKT-approach for solving bilevel problems, where the lower level minimality condition is replaced by the KKTor… (More)

- Georg Still
- Math. Program.
- 2001

- Petrica C. Pop, Walter Kern, Georg Still
- European Journal of Operational Research
- 2006

- Petrica C. Pop, Georg Still, Walter Kern
- ACiD
- 2005

Given a complete undirected graph with the nodes partitioned into m node sets called clusters, the Generalized Minimum Spanning Tree problem denoted by GMST is to find a minimum-cost tree which includes exactly one node from each cluster. It is known that the GMST problem is NP-hard and even finding a near optimal solution is NP-hard. We give an… (More)

- S. Ilker Birbil, J. B. G. Frenk, Georg Still
- European Journal of Operational Research
- 2007

In this note we give an elementary proof of the Fritz-John and Karush–Kuhn–Tucker conditions for nonlinear finite dimensional programming problems with equality and/or inequality constraints. The proof avoids the implicit function theorem usually applied when dealing with equality constraints and uses a generalization of Farkas lemma and the… (More)

- Ligong Wang, INTEGRAL TREES, Xueliang Li, Georg Still
- 1968

No part of this work may be reproduced by print, photography or any other means without the permission in writing from the author. PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Universiteit Twente, op gezag van de rector magnificus, prof. dr. Contents Acknowledgement iii Preface v 1 Introduction 1 1.1 History of integral graphs and basic… (More)