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Proper convex function - Wikipedia

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In mathematical analysis, in particular the subfields of convex analysis and optimization, a proper convex function is an extended real-valued convex function with a non-empty domain, that never takes on the value − ∞ and also is not identically equal to + ∞ . In convex analysis and variational analysis, a point (in the domain) at which some given function 𝑓 is minimized is typically sought, where 𝑓 is valued in the extended real number line [ − ∞ , ∞ ] = 𝑅 ∪ { ± ∞ } . [1] Such a point, if it exists, is called a global minimum point of the function and its value at this point is called the global minimum (value) of the function. If the function takes − ∞ as a value then − ∞ is necessarily the global minimum value and the minimization problem can be answered; this is ultimately the reason why the definition of "proper" requires that the function never take − ∞ as a value. Assuming this, if the function's domain is empty or if the function is identically equal to + ∞ t

Proper convex function - Wikipedia Jump to content From Wikipedia, the free encyclopedia Concept in convex analysis This article is about the concept in convex analysis . For the concept of properness in topology , see proper map . In mathematical analysis , in particular the subfields of convex analysis and optimization , a proper convex function is an extended real -valued convex function with a non-empty domain , that never takes on the value − ∞ {\displaystyle -\infty } and also is not identically equal to + ∞ . {\displaystyle +\infty .} In convex analysis and variational analysis , a poin

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