Theorem 1 of the following paper:
Wei Yu and Raymond Lui: "Dual Methods for Nonconvex Spectrum Optimization of
Multicarrier Systems", IEEE Transactions on Communications, vol. 54, no. 7,
pp.1310-1322, July 2006.
should have included an additional constraint qualification condition.
A correct version of the theorem is:
"Theorem 1: Consider an optimization problem of the form (4), which satisfies
Slater's condition (i.e., there exists a strictly feasible solution in the
constraint set). If the optimization problem satisfies the time-sharing
property, then it has a zero duality gap, i.e., the primal problem (4) and
the dual problem (7) have the same optimal value."
Constraint qualification (such as Slater's condition) is needed for zero
duality gap. Note that Slater's condition is always satisfied for the class
of spectrum optimization problems considered in the paper. However, constraint
qualification is needed for the general theorem.
The authors wish to acknowledge Tamas Terlaky and Jiaping Zhu for pointing out
this unintentional omission.