Minimizing Separable Convex Functions Subject to Simple Chain Constraints

Authors:
Michael J. Best;Nilotpal Chakravarti;Vasant A. Ubhaya
Affiliations:
-;-;-
Venue:
SIAM Journal on Optimization
Year:
1999

Citing 0
Cited 2

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Abstract

Minimizing a separable convex objective subject to an ordering restriction on its variables is a generalization of a class of problems in statistical estimation and inventory control. It is shown that a pool adjacent violators (PAV) algorithm can be used to compute an optimal solution of this problem as well as the minimal and maximal extended solutions, which provide lower and upper bounds on all optimal solutions and solve certain subproblems. These results unify and extend several previously known results. In addition, it is shown that a PAV algorithm can be applied to solving the problem with integer constraints on the variables.