Quadratic Programming Problems on Time Scales
In this work, we formulate and solve quadratic programming problems using the time scales approach. This approach unifies discrete and continuous quadratic programming models and extends them to other cases “in between.” The formulation of the primal as well as the dual time scales quadratic programming models has been successfully constructed on arbitrary time scales. The new formulation yields the exact optimal solution for the quadratic programming models using isolated time scales setting. Also, for the time scales setting T = R, we obtain the classical continuous-time quadratic programming problems, which means that our new formulation is an extension of the continuous-time problem. In addition, we establish the weak duality theorem and the optimality condition for arbitrary time scales, while the strong duality theorem is given for isolated time scales. Moreover, we prove these theorems by developing the time scales analogue of Dorn’s technique for quadratic programming problems. Furthermore, examples are given to illustrate the usefulness of the presented results.
R. Al-Salih and M. Bohner, "Quadratic Programming Problems on Time Scales," Applied and Computational Mathematics, vol. 19, no. 2, pp. 205-219, Elsevier, Jul 2020.
Mathematics and Statistics
Keywords and Phrases
Dual Model; Optimality Condition; Primal Model; Quadratic Programming Problem; Strong Duality Theorem; Time Scales; Weak Duality Theorem
International Standard Serial Number (ISSN)
Article - Journal
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01 Jul 2020