Fenchel duality theorem in multiobjective programming problems with set functions

2003 ◽  
Vol 13 (1-2) ◽  
pp. 139-152 ◽  
Author(s):  
Sanming Liu ◽  
Enmin Feng
Keyword(s):  
Duality Theorem ◽  
Multiobjective Programming ◽  
Fenchel Duality ◽  
Set Functions ◽  
Multiobjective Programming Problems

scholarly journals Duality in mathematical programming of set functions: On Fenchel duality theorem

1983 ◽  
Vol 95 (1) ◽  
pp. 223-234 ◽  
Author(s):  
Hang-Chin Lai ◽  
Shu-Shih Yang ◽  
George R. Hwang
Keyword(s):  
Mathematical Programming ◽  
Duality Theorem ◽  
Fenchel Duality ◽  
Set Functions

Multiobjective Programming

2014 ◽  
pp. 1585-1604
Author(s):  
Minghe Sun
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Objective Functions ◽  
Solution Quality ◽  
Solution Methods ◽  
Multiobjective Programming Problem ◽  
Feasible Solutions ◽  
Multiobjective Programming Problems

Optimization problems with multiple criteria measuring solution quality can be modeled as multiobjective programming problems. Because the objective functions are usually in conflict, there is not a single feasible solution that can optimize all objective functions simultaneously. An optimal solution is one that is most preferred by the decision maker (DM) among all feasible solutions. An optimal solution must be nondominated but a multiobjective programming problem may have, possibly infinitely, many nondominated solutions. Therefore, tradeoffs must be made in searching for an optimal solution. Hence, the DM's preference information is elicited and used when a multiobjective programming problem is solved. The model, concepts and definitions of multiobjective programming are presented and solution methods are briefly discussed. Examples are used to demonstrate the concepts and solution methods. Graphics are used in these examples to facilitate understanding.

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