Applications of variational analysis to a generalized Heron problem

References

• B.S. Mordukhovich, N.M. Nam, and J. Salinas, Solving a generalized Heron problem by means of convex analysis, Am. Math. Monthly (to appear)
   Google Scholar
• Courant , R and Robbins , R . 1941 . What is Mathematics? An Elementary Approach to Ideas and Methods , London : Oxford University Press .
   Google Scholar
• Heath , TL . 1921 . A History of Greek Mathematics , London : Oxford University Press .
   Google Scholar
• Mordukhovich , BS and Nam , NM . 2011 . Applications of variational analysis to a generalized Fermat-Torricelli problem . J. Optim. Theory Appl. , 148 : 431 – 454 .
   Web of Science ®Google Scholar
• Mordukhovich , BS and Nam , NM . 2011 . Subgradients of minimal time functions under minimal assumptions . J. Convex Anal. , 18 (to appear)
   Web of Science ®Google Scholar
• Nickel , S , Puerto , J and Rodriguez-Chia , AM . 2003 . An approach to location models involving sets as existing facilities . Math. Oper. Res. , 28 : 693 – 715 .
   Web of Science ®Google Scholar
• Mordukhovich , BS . Variational Analysis and Generalized Differentiation, I: Basic Theory, Grundlehren Series (Fundamental Principles of Mathematical Sciences), Vol. 330, Springer, Berlin, 2006
   Google Scholar
• Rockafellar , RT and Wets , RJ-B . 1998 . “ Variational Analysis ” . In Grundlehren Series (Fundamental Principles of Mathematical Sciences) , Vol. 517 , Berlin : Springer .
   Google Scholar
• Borwein , JM and Zhu , QJ . 2005 . “ Techniques of Variational Analysis ” . In , CMS Books in Mathematics , Vol. 20 , New York : Springer .
   Google Scholar
• Mordukhovich , BS . 2006 . “ Variational Analysis and Generalized Differentiation, II: Applications ” . In , Grundlehren Series (Fundamental Principles of Mathematical Sciences) , Vol. 331 , Berlin : Springer .
   Google Scholar
• Schirotzek , W . 2007 . “ Nonsmooth Analysis ” . In Universitext , Berlin : Springer .
   Google Scholar
• Mordukhovich , BS and Nam , NM . 2010 . Limiting subgradients of minimal time functions in Banach spaces . J. Global Optim. , 46 : 615 – 633 .
   Web of Science ®Google Scholar
• Fitzpatrick , S . 1980 . Metric projections and differentiability of the distance function . Bull. Austral. Math. Soc. , 20 : 291 – 312 .
   Google Scholar
• Bertsekas , D , Nedic , A and Ozdaglar , A . 2003 . Convex Analysis and Optimization , Boston , , MA : Athena Scientific .
   Google Scholar
• Boyd , S , Xiao , L and Mutapcic , A . 2003 . Subgradient Methods , Lecture Notes, Stanford University .
   Google Scholar