Table 12.

Convexity and complexity of all methods

Method	convexity	complexity
1-SVM SOCP L∞, L2	convex	O((p + n)2n2.5)
1-SVM QCQP L∞	convex	O(pn3)
SVM SOCP L∞, L2	convex	O((p + n)2(k + n)2.5)
SVM QCQP L∞	convex	O(pk2n2 + k3n3)
SVM SIP L∞	convex	O(τ(kn3 + p3))
SVM SIP L2	relaxation	O(τ(kn3 + p3))
LSSVM SOCP L∞, L2	convex	O((p + n)2(k + n)2.5)
LSSVM QCQP L∞, L2	convex	O(pk2n2 + k3n3)
LSSVM SIP L∞	convex	O(τ(n2 + p3))
LSSVM SIP L2	relaxation	O(τ(n2 + p3))

Convexity and complexity of all methods. n is the number of samples, p is the number of kernels, k is the number of classes, τ is the number of iterations in SIP. The complexity of LSSVM SIP depends on the algorithms used to solve the linear system. For the conjugate gradient method, the complexity is between O(n^1.5) and O(n²) [22].