Doctoral Dissertations

Keywords and Phrases

Duality Theorems; Programming Problems; Time Scales

Abstract

"In this dissertation, novel formulations for several classes of programming problems are derived and proved using the time scales technique. The new formulations unify the discrete and continuous programming models and extend them to other cases "in between." Moreover, the new formulations yield the exact optimal solution for the programming problems on arbitrary isolated time scales, which solve an important open problem. Throughout this dissertation, six distinct classes of programming problems are presented as follows. First, the primal as well as the dual time scales linear programming models on arbitrary time scales are formulated. Second, separated linear programming primal and dual models have been established using the time scales approach. Third, state-constraints separated linear programming primal and dual models on time scales are considered. Fourth, linear fractional primal and dual models have been constructed on time scales. Fifth, quadratic programming problems are formulated using the time scales technique. Sixth, quadratic fractional programming problems have been constructed using a hybrid of the parametric approach and the time scales technique. In addition, for each class of these programming problems the weak duality theorem and the optimality conditions theorem are established for arbitrary time scales, while the strong duality theorem is given for isolated time scales to ensure that our formulation is indeed a perfect formulation. Furthermore, examples for the most well-known isolated time scales are given to illustrate the main results"--Abstract, page iv.

Advisor(s)

Bohner, Martin, 1966-

Committee Member(s)

Akin, Elvan
He, Xiaoming
Paige, Robert
Gelles, Gregory M.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

Missouri University of Science and Technology

Publication Date

Summer 2017

Journal article titles appearing in thesis/dissertation

  • Linear programming problems on time scales
  • Separated and state-constrained linear programming problems on time scales
  • Linear fractional programming problems on time scales
  • Quadratic programming problems on time scales
  • Quadratic fractional programming problems on time scales

Pagination

viii, 141 pages

Note about bibliography

Includes bibliographic references.

Rights

© 2017 Rasheed Basheer Al-Salih, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 11335

Electronic OCLC #

1041855974

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