polar cone

English

A set C and its polar cone C^o.

Noun

polar cone (plural polar cones)

1. (linear algebra) Relative to a set S in Rⁿ, the set of points y such that the inner product of x and y is not positive for any point x in S.

   Since a is in S and b is in S^o — the polar cone of S — we know that a^T b ≤ 0.

See also

• (set of points): dual cone

References

• Vince A. Sposito and H. T. David, "A Note on Farkas Lemmas Over Cone Domains", SIAM Journal on Applied Mathematics, Vol. 22, No. 3. (May, 1972), pp. 356-358. [1]

Further reading

• Dual cone and polar cone on Wikipedia.Wikipedia