Appl Math Optim 38:239–259 (1998)
1998 Springer-Verlag New York Inc.
Relaxation Methods for Strictly Convex Regularizations
of Piecewise Linear Programs
K. C. Kiwiel
Systems Research Institute, Newelska 6,
01–447 Warsaw, Poland
Communicated by J. Stoer
Abstract. We give an algorithm for minimizing the sum of a strictly convex func-
tion and a convex piecewiselinear function. It extends several dual coordinate ascent
methods for large-scale linearly constrained problems that occur in entropy max-
imization, quadratic programming, and network ﬂows. In particular, it may solve
exact penalty versions of such (possibly inconsistent) problems, and subproblems of
bundle methods for nondifferentiable optimization. It is simple, can exploit sparsity,
and in certain cases is highly parallelizable. Its global convergence is established in
the recent framework of B-functions (generalized Bregman functions).
KeyWords. Convex programming, Entropy maximization, Nondifferentiable op-
timization, Relaxation methods, Dual coordinate ascent, B-functions.
AMS Classiﬁcation. Primary 65K05, Secondary 90C25.
We give an algorithm for the following convex programming problem:
minimize F(x) := f (x) +
f (x) (1.1a)
This research was supported by the State Committee for Scientiﬁc Research under Grant 8T11A02610.