Benson's algorithm: Difference between revisions

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{{distinguish2|[[Benson's algorithm (Go)]], a method to find the unconditionally alive stones in the game [[Go (game)|Go]]}}
 
'''Benson's algorithm''', named after [[Harold Benson]], is a method for solving [[linear programming|linear]] [[multi-objective optimizationlinear programming]] problems and vector linear programs. This works by finding the "efficient extreme points in the outcome set".<ref name="Benson">{{cite journal | author = Harold P. Benson | year = 1998 | title = An Outer Approximation Algorithm for Generating All Efficient Extreme Points in the Outcome Set of a Multiple Objective Linear Programming Problem | journal = Journal of Global Optimization | volume = 13 | issue = 1 | pages = 1–24 | doi = 10.1023/A:1008215702611 | url = https://link.springer.com/article/10.1023%2FA%3A1008215702611 | format = | accessdate = September 21, 2013}}</ref> The primary concept in Benson's algorithm is to evaluate the upper image of the [[vector optimization]] problem by [[cutting-plane method|cutting planes]].<ref name="Lohne">{{cite book|title=Vector Optimization with Infimum and Supremum|author=Andreas Löhne|publisher=Springer|year=2011|isbn=9783642183508|pages=162–169}}</ref>
 
== Idea of algorithm ==