In constrained optimization, a field of mathematics, a barrier function is a continuous function whose value on a point increases to infinity as theâ€¦Â (More)

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2015

2015

- Xiangru Xu, Paulo Tabuada, Jessy W. Grizzle, Aaron D. Ames
- ArXiv
- 2015

Barrier functions (also called certificates) have been an important tool for the verification of hybrid systems, and have alsoâ€¦Â (More)

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2014

Highly Cited

2014

- Aaron D. Ames, Jessy W. Grizzle, Paulo Tabuada
- 53rd IEEE Conference on Decision and Control
- 2014

This paper develops a control methodology that unifies control barrier functions and control Lyapunov functions through quadraticâ€¦Â (More)

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2011

2011

- Unsik Lee, Mehran Mesbahi
- IEEE Conference on Decision and Control andâ€¦
- 2011

In this paper, we consider distributed algorithms for consensus of multiple agents in presence of convex state constraints onâ€¦Â (More)

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2006

2006

- Joshua Hauser, Alessandro Saccon
- Proceedings of the 45th IEEE Conference onâ€¦
- 2006

We develop a barrier function method for the optimization of trajectory functionals with constraints. An approximate or relaxedâ€¦Â (More)

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2004

2002

2002

- Stephen J. Wright, Dominique Orban
- Math. Oper. Res.
- 2002

Abstract. We examine the sequence of local minimizers of the log-barrier function for a nonlinear program near a solution atâ€¦Â (More)

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1997

Highly Cited

1997

- Aharon Ben-Tal, Michael Zibulevsky
- SIAM Journal on Optimization
- 1997

We study a class of methods for solving convex programs, which are based on nonquadratic Augmented Lagrangians for which theâ€¦Â (More)

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1996

Highly Cited

1996

- Osman GÃ¼ler
- Math. Oper. Res.
- 1996

We show that the universal barrier function of a convex cone introduced by Nesterov and Nemirovskii is the logarithm of theâ€¦Â (More)

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1996

Highly Cited

1996

- Roberta Paladini, K. Takahashi, Natalia Bravo, Pierre A. Coulombe
- The Journal of cell biology
- 1996

Injury to stratified epithelia causes a strong induction of keratins 6 (K6) and 16 (K16) in post-mitotic keratinocytes located atâ€¦Â (More)

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1992

Highly Cited

1992

- Roman A. Polyak
- Math. Program.
- 1992

The nonlinear rescaling principle employs monotone and sufficiently smooth functions to transform the constraints and/or theâ€¦Â (More)

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