Name
Abstract | ||
|---|---|---|
We consider the general optimization problem (P ) of selecting a continuous functionx over aæ-compact Hausdorfi space T to a metric space A, from a feasible region X of such functions, so as to minimize a functional c on X. We require that X consist of a closed equicontinuous family of functions lying in the product (over T )o f compact subsets Yt of A. (An important special case is the optimal control problem of flnding a continuous time control function x that minimizes its associated discounted cost c(x) over the inflnite horizon.) Relative to the uniform-on-compacta topology on the function space C(T;A) of continuous functions from T to A, the feasible region X is compact. Thus optimal solutions x⁄ to (P ) exist under the assumption that c is continuous. We wish to approximate such an x⁄ by optimal solutions to a netfPigi 2 I of approximating problems of the form minx2Xi ci(x) for each i2 I, where (1) the net of setsfXigI converges to X in the sense of Kuratowski and (2) the netfcigI of functions converges to c uniformly on X. We show that for large i, any optimal solution x⁄i to the approximating problem (Pi) arbitrarily well approximates some optimal solution x⁄ to (P ). It follows that if (P ) is well-posed, i.e., lim supX⁄i is a singletonfx ⁄g, then any netfx⁄igI of (Pi)-optimal solutions converges in C(T;A )t o x⁄. For this case, we construct a flnite algorithm with the following property: given any prespecifled error - and any compact subset Q of T , our algorithm computes an i in I and an associated x⁄i in X ⁄ i which is within - of x⁄ on Q. We illustrate the theory and algorithm with a problem in continuous time production control over an inflnite horizon. |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1023/A:1010964322204 | Annals OR |
Keywords | Field | DocType |
continuous time optimization,optimal control,infinite horizon optimization,production control | Infinite-dimensional optimization,Function space,Feasible region,Optimization problem,Continuous function,Discrete mathematics,Mathematical optimization,Combinatorics,Algorithm,Hausdorff space,Metric space,Equicontinuity,Mathematics | Journal |
Volume | Issue | ISSN |
101 | 1-4 | 1572-9338 |
Citations | PageRank | References |
1 | 0.42 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Irwin E. Schochetman | 1 | 51 | 8.60 |
| Robert L. Smith | 2 | 664 | 123.86 |