We demonstrate that a conic quadratic problem.
(CQP)
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is "polynomially reducible" to Linear Programming.
We demonstrate this by constructing, for every epsilon is an element of (0,
1/2], an LP program (explicitly given in terms of epsilon and the data of
(CQP))
(LP)
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with the following properties:
(i) the number dim x + dim u of variables and the number dim p of constrain
ts in (LP) do not exceed
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(ii) every Feasible solution x to (CQP) can be extended to a feasible solut
ion (x, u) to (LP);
(iii) if (x, u) is feasible for (LP), then x satisfies the "epsilon -relaxe
d" constraints of (CQP), namely,
Ax greater than or equal to b, parallel toA(l)x - b(l)parallel to (2) less
than or equal to (1 + epsilon)[c(l)(t)x - d(l)], l = 1.....m.