Separated and State-Constrained Separated Linear Programming Problems on Time Scales
Separated linear programming problems can be used to model a wide range of real-world applications such as in communications, manufacturing, transportation, and so on. In this paper, we investigate novel formulations for two classes of these problems using the methodology of time scales. As a special case, we obtain the classical separated continuous-time model and the state-constrained separated continuous-time model. We establish some of the fundamental theorems such as the weak duality theorem and the optimality condition on arbitrary time scales, while the strong duality theorem is presented for isolated time scales. Examples are given to demonstrate our new results.
R. Al-Salih and M. Bohner, "Separated and State-Constrained Separated Linear Programming Problems on Time Scales," Boletim da Sociedade Paranaense de Matematica, vol. 38, no. 4, pp. 181-195, Boletim da Sociedade Paranaense de Matematica, Jan 2020.
The definitive version is available at https://doi.org/10.5269/bspm.v38i4.40414
Mathematics and Statistics
Keywords and Phrases
Optimality condition; Separated linear programming problem; State constrained; Strong duality theorem; Time scales; Weak duality theorem
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 2020