A strong duality theorem for the minimum of a family of convex programs

1980 ◽  
Vol 31 (4) ◽  
pp. 453-472 ◽  
Author(s):  
J. M. Borwein
Keyword(s):  
Duality Theorem ◽  
Strong Duality ◽  
Convex Programs

Strong duality for standard convex programs

2021 ◽  
Author(s):  
Kenneth O. Kortanek ◽  
Guolin Yu ◽  
Qinghong Zhang
Keyword(s):  
Strong Duality ◽  
Convex Programs

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.

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