Dual Problems and Separation of Sets: Lagrange and Fenchel Duality

1997 ◽  
Vol 93 (1) ◽  
pp. 227-231 ◽  
Author(s):  
C. Antoni
1993 ◽  
Vol 2 (1) ◽  
pp. 11-23 ◽  
Author(s):  
John Gates

A definition is adopted for convexity of a set of directed lines in the plane. Following this, the duals of a number of standard problems of geometric probability are formulated. Problems considered in detail are the duals of Sylvester's problem, chord length distributions and Ambartzumian's combinatorial geometry. The paper suggests some questions for further work.


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