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Convex cone

It often means a cone that satisfies other properties like being convex, closed, pointed, salient, and full-dimensional. A type of cone of particular interest to pure mathematicians is the partially ordered set of rational cones. A cone is called rational here we assume "pointed", as defined above whenever its generators all have integer coordinates, i. The continuous or topological dual cone to C is the set.

Convex cone - Wikipedia

If C is equal to its dual cone, then C is called self-dual. A cone can be said to be self-dual without reference to any given inner product, if there exists an inner product with respect to which it is equal to its dual by the first definition. Sums and positive scalar multiples of valid inequalities with respect to this order remain valid inequalities.

A vector space with such an order is called an ordered vector space. Such an ordering is commonly found in positive semidefinite programming. From Wikipedia, the free encyclopedia. Theory, Facts, and Formulas Second Edition.

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Encyclopedic Dictionary of Mathematics. Fundamentals of Convex Analysis. Theory of Linear and Integer Programming. Polytopes, Rings and K-Theory 1 ed. Springer Monographs in Mathematics.

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Monomial Algebras, Second Edition. Optimality Conditions in Convex Optimization: A Theory of Necessary Conditions. Generalized Convexity and Generalized Monotonicity: Introduction to Linear and Convex Programming.

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