Consider the linear continuous time programming problem / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / subject to / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / and / z(t) (GREATERTHEQ) 0, t (ELEM) {0, T}. / The vector function z(t) maps {0, T} into R('n), a(t) is an n-dimensional row-vector and c(t) is an m-dimensional column vector. The matrices B(t) and K(t, s) are of dimension mxn. / We show that under certain conditions the optimal solution contains at most m positive elements, for almost all t (ELEM) {0, T}. This makes it possible to express the solution as an infinite matrix series. One property of the solutions is that the vector function z(t) is not necessarily smooth for all t at optimum. Rather, different components may be positive over different intervals. The points at which the change occurs are called join points. We show that all join points are natural, that is they occur when a variable goes to zero either in the original problem or in an associated dual problem. / Our approach leads to a confirmation of a conjecture about the smoothness of solutions between join points. We also prove a conjecture which had been made about the behavior of the solutions as t (--->) (INFIN). / The previous developments lead to an algorithm for the problem. The algorithm makes use of the simplex method to obtain solutions using a matrix series. The method is incorporated in a computer program and examples are given. / We discuss the nonlinear problem and prove a theorem on the convergence of a penalty function approach on a precompact metric space. / Source: Dissertation Abstracts International, Volume: 42-10, Section: B, page: 4168. / Thesis (Ph.D.)--The Florida State University, 1981.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_74678 |
| Contributors | JOHANNESSON, BENEDIKT., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 124 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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