The primal problems for finding these two hyperplanes are two convex quadratic programming problems (Shao et al.

It has become one of the popular methods in machine learning because of its low computational complexity, since it solves above two smaller sized convex quadratic programming problems.

It's dual problem is also a convex quadratic programming problem.

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] Its dual problem is the following convex quadratic programming

For the case of p = 0, [parallel] w [[parallel].sub.0] represents the number of nonzero components of w, for the case of p = 0, the problem turns to be a linear programming, for the case of p = 2, a convex quadratic programming, and for the case of p = [infinity], the problem is proved to be equivalent to a linear programming problem (Zou, Yuan 2008).

For the problem of scheduling unrelated parallel machines in the absence of nontrivial release dates R [parallel] [Sigma] [w.sub.j][C.sub.j], we introduce a convex quadratic programming relaxation that leads to a simple 3/2-approximation algorithm.

In particular, we derive a convex quadratic programming relaxation in [n.sup.2]m assignment variables and O(nm) constraints.

Lemma 2.4 and the remarks above motivate the consideration of the following convex quadratic programming relaxation (CQP):

Furthermore, if we remove constraints (19) and replace [C.sub.j] in the objective function by the right-hand side of (19), we get the following convex quadratic programming relaxation, which we denote by (CQP) since it generalizes the convex quadratic program developed in Section 2: