Probabilistic Constrained Linear Programming: Duality Theory

2012 ◽  
Keyword(s):  
Linear Programming ◽  
Duality Theory ◽  
Linear Programming Duality

Lower bounds for two-period grooming via linear programming duality

Networks ◽  
2008 ◽  
Vol 52 (4) ◽  
pp. 299-306 ◽  
Author(s):  
Charles J. Colbourn ◽  
Gaetano Quattrocchi ◽  
Violet R. Syrotiuk
Keyword(s):  
Linear Programming ◽  
Lower Bounds ◽  
Linear Programming Duality

scholarly journals A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xue-Gang Zhou ◽  
Bing-Yuan Cao
Keyword(s):  
Linear Programming ◽  
Branch And Bound ◽  
Duality Theory ◽  
Global Minimum ◽  
Auxiliary Variables ◽  
Multiplicative Programming ◽  
Branch And Bound Search ◽  
Linear Multiplicative Programming ◽  
Linear Programming Problems ◽  
Present Algorithm

A simplicial branch and bound duality-bounds algorithm is presented to globally solving the linear multiplicative programming (LMP). We firstly convert the problem (LMP) into an equivalent programming one by introducingpauxiliary variables. During the branch and bound search, the required lower bounds are computed by solving ordinary linear programming problems derived by using a Lagrangian duality theory. The proposed algorithm proves that it is convergent to a global minimum through the solutions to a series of linear programming problems. Some examples are given to illustrate the feasibility of the present algorithm.

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