Feb 23, 2016 · Secondorder cone programming (SOCP) formulations have received increasing attention as robust optimization schemes for Support Vector Machine (SVM) classifiion. These formulations study the worstcase setting for classconditional densities, leading to potentially more effective classifiers in terms of performance compared to the standard SVM formulation. .
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Feb 18, 2018 · 1 Answer. I don't think they're the same. A x ⪯ K b A x − b ⪯ K 0 − ( A x − b) ∈ K. So if K were the positive orthant, then we'd have the standard affine constraint A x − b ≤ 0. A secondorder (Lorentz) cone is defined by L n := { ( x, t): ‖ x ‖ 2 ≤ t, t ≥ 0, x ∈ R n }, so x ~ = ( x, t) ∈ L n x ~ ⪰ L n 0, ...
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Apr 08, 2021 · The set in Rn+1 R n + 1. Kn:={(x,y) ∈Rn+1:y ≥ ∥x∥2} K n := { ( x, y) ∈ R n + 1: y ≥ ‖ x ‖ 2 } is a convex cone, called the secondorder cone. Example: The secondorder cone is sometimes called ''icecream cone''. In R3 R 3, it is the set of triples (x1,x2,y) ( x 1, x 2, y) with. y2 ≥ x2 1 +x2 2, y ≥ 0. y 2 ≥ x 1 2 ...
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Dec 26, 2015 · Second Order Cone Program. I am trying to solve the following optimization problem ( Problem ) which can be setup as an SOCP. I can further simplify it by multiplying the inequality constraint by x, which is positive, and thus the inequality remains unchanged. Then we substitute, u = x on the righthand side to get the following problem.
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