Algorithmic Aspects of Convex Sets: Formulation of the Problems
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Given a point y and a set K, is y a member of K, i. e., is y contained in K?
If y is not a member of K, find a hyperplane separating y from K.
Given a linear inequality, is it valid for each vector in K?
Given a linear function, find a point maximizing (or minimizing) the function on K.
Given a convex function, find its minimum.
KeywordsConvex Body Rational Number Separation Problem Separation Algorithm Membership Problem
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