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Second-order cone programming - University of Chicago

Math. Program., Ser. B 95: 3 51 (2003)Digital Object Identifier (DOI) Alizadeh D. Goldfarb Second-order cone programmingReceived: August 18, 2001 / Accepted: February 27, 2002 Published online: December 9, 2002 c Springer-Verlag 20021. IntroductionSecond-order cone programming (SOCP) problems are convex optimization problemsin which a linear function is minimized over the intersection of an affine linear manifoldwith the Cartesian product of Second-order (Lorentz) cones. Linear programs, convexquadratic programs and quadratically constrained convex quadratic programs can allbe formulated as SOCP problems, as can many other problems that do not fall intothese three categories.

Feb 27, 2002 · 6 F. Alizadeh, D. Goldfarb For two matrices Aand B, A⊕ Bdef= A0 0 B Let K ⊆ kbe a closed, pointed (i.e. K∩(−K)={0}) and convex cone with nonempty interior in k; in this article we exclusively work with such cones.It is well-known that K induces a partial order on k: x K y iff x − y ∈ K and x K y iff x − y ∈ int K The relations K and ≺K are defined similarly. For each cone ...

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