On Polyhedral Approximations of the Second-Order Cone

Authors:
Aharon Ben-Tal;Arkadi Nemirovski
Affiliations:
-;-
Venue:
Mathematics of Operations Research
Year:
2001

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Abstract

We demonstrate that a conic quadratic problem, is "polynomially reducible" to Linear Programming. We demonstrate this by constructing, for every , an LP program (explicitly given in terms of e and the data of (CQP)) with the following properties:(i)the number dimx + dimu of variables and the number dimp of constraints in (LP) do not exceed (ii)every feasible solutionx to (CQP) can be extended to a feasible solution ( x, u) to (LP); (iii)if ( x, u) is feasible for (LP), thenx satisfies the "e-relaxed" constraints of (CQP), namely,