The Set of Target Vectors in a Semi-Infinite Linear Program with a Duality Gap

2019 ◽  
Vol 304 (S1) ◽  
pp. S14-S22
Author(s):  
N. N. Astaf’ev ◽  
A. V. Ivanov ◽  
S. P. Trofimov
Keyword(s):  
Linear Program ◽  
Duality Gap ◽  
Infinite Linear

An Infinite Linear Program with a Duality Gap

1965 ◽  
Vol 12 (1) ◽  
pp. 122-134 ◽  
Author(s):  
R. J. Duffin ◽  
L. A. Karlovitz
Keyword(s):  
Linear Program ◽  
Duality Gap ◽  
Infinite Linear

scholarly journals The Use of the Duality Principle to Solve Optimization Problems

2018 ◽  
Vol 6 (1) ◽  
pp. 33
Author(s):  
Rowland Jerry Okechukwu Ekeocha ◽  
Chukwunedum Uzor ◽  
Clement Anetor
Keyword(s):  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Linear Program ◽  
Duality Gap ◽  
Duality Principle ◽  
Primal Problem ◽  
Optimal Values ◽  
Primal And Dual Problems ◽  
Primal And Dual

<p><span>The duality principle provides that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. The solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem. However the optimal values of the primal and dual problems need not be equal. Their difference is called the duality gap. For convex optimization problems, the duality gap is zero under a constraint qualification condition.<span>  </span>In other words given any linear program, there is another related linear program called the dual. In this paper, an understanding of the dual linear program will be developed. This understanding will give important insights into the algorithm and solution of optimization problem in linear programming. <span> </span>Thus the main concepts of duality will be explored by the solution of simple optimization problem.</span></p>

Spare simple MKKM with semi‐infinite linear program optimization

2021 ◽  
Author(s):  
Yuxin Huang ◽  
Miaomiao Li ◽  
Wenxuan Tu ◽  
Jiyuan Liu ◽  
Jiahao Ying
Keyword(s):  
Linear Program ◽  
Program Optimization ◽  
Infinite Linear

Zero duality gap conditions via abstract convexity∗

Optimization ◽  
2021 ◽  
pp. 1-37
Author(s):  
Hoa T. Bui ◽  
Regina S. Burachik ◽  
Alexander Y. Kruger ◽  
David T. Yost
Keyword(s):  
Duality Gap ◽  
Abstract Convexity ◽  
Zero Duality Gap
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