The benchmarks are related to no-bias data classification, i.e., we do not consider the bias of the hyperplane in a classification model. However we include it by means of augmenting w = [w; B] and x = [x; b]. Then, the SVM dual formulations result into

(1) argmin 1/2 a' H a - a' e s.t. 0 <= a <= Ce

(2) argmin 1/2 a' H a - a' e s.t. 0 <= a

for l1-loss and l2-loss, respectively. The classification dataset, namely mushrooms and phishing, were downloaded from the LIBSVM dataset page.

Displacement of a string with fixed ends subject to the lower bound. Solved as finite differences discretization of

-u''(x) = -15,  x in [0,1]
u(0) = u(1) = 0
s.t. u(x) > sin(4*pi*x -pi/6)/2 -2

Displacement of a string with fixed ends subject to the lower bound on the first half of the domain. Solved as finite differences discretization of

-u''(x) = -15,  x in [0,1]
u(0) = u(1) = 0
s.t. u(x) > sin(4*pi*x -pi/6)/2 -2, x in [0,1/2]

Pressure distribution in a journal bearing from MINPACK-2 (epsilon = 0.1, b = 10). See http://ftp.mcs.anl.gov/pub/tech_reports/reports/P153.pdf, section 4.2, page 33.

The problem has only a lower bound. The provided upper bound is set to constant vector = 1000 and can be ignored.