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Directional End of a Convex Set: Theory and Applications

Author

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  • M. A. Goberna
  • V. Jornet
  • M. Rodríguez

Abstract

A point of a convex set belongs to its end in a given direction when this direction is not feasible at that point. This paper analyzes the properties of the directional end of general convex sets and closed convex sets (for which the directional ends are connected by arcs) as well as the relationship between the directional end and certain concepts on the illumination of convex bodies. The paper includes applications of the directional end to the theory of linear systems.

Suggested Citation

  • M. A. Goberna & V. Jornet & M. Rodríguez, 2001. "Directional End of a Convex Set: Theory and Applications," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 389-411, August.
    • Handle: RePEc:spr:joptap:v:110:y:2001:i:2:d:10.1023_a:1017583514580
    DOI: 10.1023/A:1017583514580
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    References listed on IDEAS

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    1. Rubén Puente & Virginia Vera de Serio, 1999. "Locally Farkas-Minkowski linear inequality systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 103-121, June.
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