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conic optimization : ウィキペディア英語版
conic optimization

Conic optimization is a subfield of convex optimization that studies a class of structured convex optimization problems called conic optimization problems. A conic optimization problem consists of minimizing a convex function over the intersection of an affine subspace and a convex cone.
The class of conic optimization problems is a subclass of convex optimization problems and it includes some of the most well known classes of convex optimization problems, namely linear and semidefinite programming.
==Definition==

Given a real vector space ''X'', a convex, real-valued function
:f:C \to \mathbb R
defined on a convex cone C \subset X, and an affine subspace \mathcal defined by a set of affine constraints h_i(x) = 0 \ , a conic optimization problem is to find the point x in C \cap \mathcal for which the number f(x) is smallest.
Examples of C include the positive orthant \mathbb_+^n = \left\\right\} , positive semidefinite matrices \mathbb^n_, and the second-order cone \left \\times \mathbb : \lVert x \rVert \leq t \right \} . Often f \ is a linear function, in which case the conic optimization problem reduces to a semidefinite program, a linear program, and a second order cone program, respectively.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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