Browsing by Author "Rothblum, Uriel G."

Now showing 1 - 4 of 4

A new approach to solve open-partition problems
(2012-01-01)
Chang, Huilan
;
Hwang, Frank K.
;
Rothblum, Uriel G.
;
應用數學系
;
Department of Applied Mathematics
A partition problem in one-dimensional space is to seek a partition of a set of numbers that maximizes a given objective function. In some partition problems, the partition size, i.e., the number of nonempty parts in a partition, is fixed; while in others, the size can vary arbitrarily. We call the former the size-partition problem and the latter the open-partition problem. In general, it is much harder to solve open problems since the objective functions depend on size. In this paper, we propose a new approach by allowing empty parts and transform the open problem into a size problem allowing empty parts, called a relaxed-size problem. While the sortability theory has been established in the literature as a powerful tool to attack size partition problems, we develop the sortability theory for relaxed-size problems as a medium to solve open problems.
A polytope approach to the optimal assembly problem
(2006-07-01)
Hwang, Frank K.
;
Rothblum, Uriel G.
;
應用數學系
;
Department of Applied Mathematics
The problem of assembling components into series modules to maximize the system reliability has been intensively studied in the literature. Invariably, the methods employed exploit special properties of the reliability function through standard analytical optimization techniques. We propose a geometric approach by exploiting the assembly polytope - a polytope generated by the potential assembly configurations. The new approach yields simpler proofs of known results, as well as new results about systems where the number of components in a module is not fixed, but subject to lower and upper bounds.
Equivalence of permutation polytopes corresponding to strictly supermodular functions
(2008-06-28)
Hwang, Frank K.
;
Lee, J. S.
;
Rothblum, Uriel G.
;
應用數學系
;
Department of Applied Mathematics
This paper demonstrates a strong equivalence of all permutation polytopes corresponding to strictly supermodular functions. (C) 2007 Elsevier B.V. All rights reserved.
The mean-partition problem
(2006-09-01)
Chang, Fei-Hwang
;
Hwang, Frank K.
;
Rothblum, Uriel G.
;
應用數學系
;
Department of Applied Mathematics
In mean-partition problems the goal is to partition a finite set of elements, each associated with a d-vector, into p disjoint parts so as to optimize an objective, which depends on the averages of the vectors that are assigned to each of the parts. Each partition is then associated with a d x p matrix whose columns are the corresponding averages and a useful approach in studying the problem is to explore the mean-partition polytope, defined as the convex hull of the set of matrices associated with feasible partitions.