An Extended Duality Theorem for Continuous Linear Programming Problems

1967 ◽  
Vol 15 (5) ◽  
pp. 1294-1298 ◽  
Author(s):  
William F. Tyndall
Keyword(s):  
Linear Programming ◽  
Duality Theorem ◽  
Continuous Linear ◽  
Continuous Linear Programming ◽  
Linear Programming Problems

scholarly journals Linear programming problems on time scales

2018 ◽  
Vol 12 (1) ◽  
pp. 192-204 ◽  
Author(s):  
Rasheed Al-Salih ◽  
Martin Bohner
Keyword(s):  
Linear Programming ◽  
Optimality Conditions ◽  
Time Scales ◽  
Duality Theorem ◽  
Strong Duality ◽  
Programming Models ◽  
Weak Duality ◽  
Continuous Linear ◽  
Arbitrary Time ◽  
Linear Programming Problems

In this work, we study linear programming problems on time scales. This approach unifies discrete and continuous linear programming models and extends them to other cases ?in between?. After a brief introduction to time scales, we formulate the primal as well as the dual time scales linear programming models. Next, we establish and prove the weak duality theorem and the optimality conditions theorem for arbitrary time scales, while the strong duality theorem is established for isolated time scales. Finally, examples are given in order to illustrate the effectiveness of the presented results.

Sign in / Sign up

Export Citation Format

Share Document