Second-order cone programming: Difference between revisions

Revision as of 09:23, 1 August 2025

Revision as of 15:09, 1 August 2025

Line 14:

The name "second-order cone programming" comes from the nature of the individual constraints, which are each of the form:

::<math>\lVert A_iA x + b_ib \rVert_2 \leq c_ic^T x + d_id</math>

These each define a subspace that is bounded by an inequality based on a [[Degree of a polynomial|second-order polynomisl]] function defined on the optimization variable <math>x</math>; this can be shown to define a [[convex cone]], hence the name "'''second-order cone'''".<ref>{{Cite journal |last=Jibrin |first=Shafiu |last2=Swift |first2=James W. |date=2024 |title=On Second-Order Cone Functions |url=https://onlinelibrary.wiley.com/doi/abs/10.1155/2024/7090058 |journal=Journal of Optimization |language=en |volume=2024 |issue=1 |pages=7090058 |doi=10.1155/2024/7090058 |issn=2314-6486}}</ref> By the definition of convex cones, their intersection can also be shown to be a convex cone, although not necessarily one that can be defined by a single second-order inequality. See below for a more detailed treatment.