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  2. Convex cone - Wikipedia

    en.wikipedia.org/wiki/Convex_cone

    An affine convex cone is the set resulting from applying an affine transformation to a convex cone. [8] A common example is translating a convex cone by a point p: p + C. Technically, such transformations can produce non-cones. For example, unless p = 0, p + C is not a linear cone. However, it is still called an affine convex cone.

  3. Cone - Wikipedia

    en.wikipedia.org/wiki/Cone

    The definition of a cone may be extended to higher dimensions; see convex cone. In this case, one says that a convex set C in the real vector space R n {\displaystyle \mathbb {R} ^{n}} is a cone (with apex at the origin) if for every vector x in C and every nonnegative real number a , the vector ax is in C . [ 2 ]

  4. Invariant convex cone - Wikipedia

    en.wikipedia.org/wiki/Invariant_convex_cone

    In mathematics, an invariant convex cone is a closed convex cone in a Lie algebra of a connected Lie group that is invariant under inner automorphisms. The study of such cones was initiated by Ernest Vinberg and Bertram Kostant .

  5. Recession cone - Wikipedia

    en.wikipedia.org/wiki/Recession_cone

    In mathematics, especially convex analysis, the recession cone of a set is a cone containing all vectors such that recedes in that direction. That is, the set extends outward in all the directions given by the recession cone.

  6. Dual cone and polar cone - Wikipedia

    en.wikipedia.org/wiki/Dual_cone_and_polar_cone

    A cone C in a vector space X is said to be self-dual if X can be equipped with an inner product ⋅,⋅ such that the internal dual cone relative to this inner product is equal to C. [3] Those authors who define the dual cone as the internal dual cone in a real Hilbert space usually say that a cone is self-dual if it is equal to its internal dual.

  7. Power cone - Wikipedia

    en.wikipedia.org/wiki/Power_cone

    In linear algebra, a power cone is a kind of a convex cone that is particularly important in modeling convex optimization problems. [1] [2] It is a generalization of the quadratic cone: the quadratic cone is defined using a quadratic equation (with the power 2), whereas a power cone can be defined using any power, not necessarily 2.

  8. Second-order cone programming - Wikipedia

    en.wikipedia.org/wiki/Second-order_cone_programming

    A second-order cone program (SOCP) is a convex optimization problem of the form minimize ...

  9. Convex set - Wikipedia

    en.wikipedia.org/wiki/Convex_set

    The convex-hull operation is needed for the set of convex sets to form a lattice, in which the "join" operation is the convex hull of the union of two convex sets ⁡ ⁡ = ⁡ = ⁡ (⁡ ⁡ ()). The intersection of any collection of convex sets is itself convex, so the convex subsets of a (real or complex) vector space form a complete lattice .