Name
Abstract | ||
|---|---|---|
The property that an optimal solution to the problem of minimizing a continuous concave function over a compact convex set in Rn is attained at an extreme point is generalized by the Bauer Minimum Principle to the infinite dimensional context. The problem of approximating and characterizing infinite dimensional extreme points thus becomes an important problem. Consider now an infinite dimensional compact convex set in the nonnegative orthant of the product space Rinfinity. We show that the sets of extreme points EN of its corresponding finite dimensional projections onto RN converge in the product topology to the closure of the set of extreme points E of the infinite dimensional set. As an application, we extend the concept of total unimodularity to infinite systems of linear equalities in nonnegative variables where we show when extreme points inherit integrality from approximating finite systems. An application to infinite horizon production planning is considered. |
Year | DOI | Venue |
|---|---|---|
1998 | 10.1287/moor.23.2.433 | Math. Oper. Res. |
Keywords | DocType | Volume |
approximating extreme points,infinite dimensional compact convex,inflnite dimensional total unimodularity.,finite system,extreme point,extreme points e,inflnite dimensional convex sets,extreme points,infinite dimensional set,important problem,infinite dimensional convex sets,corresponding finite dimensional projection,projections,compact convex,infinite dimensional extreme point,infinite dimensional context | Journal | 23 |
Issue | ISSN | Citations |
2 | 0364-765X | 3 |
PageRank | References | Authors |
0.56 | 5 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| William P. Cross | 1 | 3 | 0.56 |
| H. Edwin Romeijn | 2 | 769 | 83.88 |
| Robert L. Smith | 3 | 664 | 123.86 |