Strong duality theorem

2011 ◽  
Keyword(s):  
Duality Theorem ◽  
Strong Duality

scholarly journals Strong duality theorem for multiobjective higher order nondifferentiable symmetric dual programs

2013 ◽  
Vol 9 (3) ◽  
pp. 525-530 ◽  
Author(s):  
Xinmin Yang ◽  
◽  
Jin Yang ◽  
Heung Wing Joseph Lee ◽  
◽  
...  
Keyword(s):  
Duality Theorem ◽  
Strong Duality ◽  
Higher Order

scholarly journals Separated and state-constrained separated linear programming problems on time scales

2019 ◽  
Vol 38 (4) ◽  
pp. 181-195 ◽  
Author(s):  
Rasheed Al-Salih ◽  
Martin J. Bohner
Keyword(s):  
Linear Programming ◽  
Time Scales ◽  
Continuous Time ◽  
Duality Theorem ◽  
Strong Duality ◽  
Continuous Time Model ◽  
Time Model ◽  
Wide Range ◽  
Linear Programming Problems ◽  
Fundamental Theorems

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

scholarly journals Approximate dual and approximate vector variational inequality for multiobjective optimization

1989 ◽  
Vol 47 (3) ◽  
pp. 418-423 ◽  
Author(s):  
G.–Y. Chen ◽  
B. D. Craven
Keyword(s):  
Variational Inequality ◽  
Multiobjective Optimization ◽  
Duality Theorem ◽  
Optimization Problem ◽  
Strong Duality ◽  
Vector Variational Inequality ◽  
Weak Duality ◽  
Multiobjective Optimization Problem ◽  
Feasible Set

AbstractAn approximate dual is proposed for a multiobjective optimization problem. The approximate dual has a finite feasible set, and is constructed without using a perturbation. An approximate weak duality theorem and an approximate strong duality theorem are obtained, and also an approximate variational inequality condition for efficient multiobjective solutions.

A note on strong duality theorem for a multiobjective higher order nondifferentiable symmetric dual programs

OPSEARCH ◽  
2015 ◽  
Vol 53 (1) ◽  
pp. 151-156
Author(s):  
Indira P. Debnath ◽  
S. K. Gupta ◽  
I. Ahmad
Keyword(s):  
Duality Theorem ◽  
Strong Duality ◽  
Higher Order

scholarly journals Two types of duality in multiobjective fractional programming

1996 ◽  
Vol 54 (1) ◽  
pp. 99-114 ◽  
Author(s):  
L. Coladas ◽  
Z. Li ◽  
S. Wang
Keyword(s):  
Fractional Programming ◽  
Duality Theorem ◽  
Strong Duality ◽  
Weak Duality ◽  
Multiobjective Fractional Programming ◽  
Dual Problems ◽  
Fractional Program ◽  
Mild Assumption

In this paper, we tire concerned with duality of a multiobjective fractional program. Two different dual problems are introduced with respect to the primal multiobjective fractional program. Under a mild assumption, we prove a weak duality theorem and a strong duality theorem for each type of duality. Finally, we explore some relations between these two types of duality.

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.

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