Conic optimization

Conic optimization is a subfield of convex optimization that studies problems consisting of minimizing a convex function over the intersection of an affine subspace and a convex cone.The class of conic optimization problems includes some of the most well known classes of convex optimization problems, namely linear and semidefinite programming.Given a real vector space X, a convex, real-valued function defined on a convex conedefined by a set of affine constraints, a conic optimization problem is to find the pointCertain special cases of conic optimization problems have notable closed-form expressions of their dual problems.The dual of the conic linear program is whereWhilst weak duality holds in conic linear programming, strong duality does not necessarily hold.[1] The dual of a semidefinite program in inequality form is given by
convex optimizationconvex functionaffine subspaceconvex conelinearsemidefinite programmingvector spaceconvexfunctionaffineorthantpositive semidefinitelinear programsemidefinite programsecond order cone programdual cone