Multiobjective programming problems with (G,C,α,ρ,d)-convexity

2021 ◽  
Vol 8 (1) ◽  
pp. 1-15
Author(s):  
Xiaoling Liu ◽  
Dehui Yuan
Keyword(s):  
Multiobjective Programming ◽  
Multiobjective Programming Problems

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.

Variants for the logarithmic-quadratic proximal point scalarization method for multiobjective programming

2018 ◽  
Vol 11 (06) ◽  
pp. 1850081
Author(s):  
Rómulo Castillo ◽  
Clavel Quintana
Keyword(s):  
Convex Functions ◽  
Multiobjective Programming ◽  
Proximal Point Method ◽  
Test Problems ◽  
Proximal Point ◽  
Pareto Solution ◽  
Positive Orthant ◽  
Scalarization Method ◽  
Weak Pareto Solution ◽  
Multiobjective Programming Problems

We consider the proximal point method for solving unconstrained multiobjective programming problems including two families of real convex functions, one of them defined on the positive orthant and used for modifying a variant of the logarithm-quadratic regularization introduced recently and the other for defining a family of scalar representations based on 0-coercive convex functions. We show convergent results, in particular, each limit point of the sequence generated by the method is a weak Pareto solution. Numerical results over fourteen test problems are shown, some of them with complicated pareto sets.

scholarly journals Continuous-Time Multiobjective Optimization Problems via Invexity

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
Valeriano A. De Oliveira ◽  
Marko A. Rojas-Medar
Keyword(s):  
Continuous Time ◽  
Efficient Solution ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Weakly Efficient Solution ◽  
Multiobjective Problems ◽  
Multiobjective Optimization Problems ◽  
Relationship Of ◽  
The Relationship ◽  
Multiobjective Programming Problems

We introduce some concepts of generalized invexity for the continuous-time multiobjective programming problems, namely, the concepts of Karush-Kuhn-Tucker invexity and Karush-Kuhn-Tucker pseudoinvexity. Using the concept of Karush-Kuhn-Tucker invexity, we study the relationship of the multiobjective problems with some related scalar problems. Further, we show that Karush-Kuhn-Tucker pseudoinvexity is a necessary and suffcient condition for a vector Karush-Kuhn-Tucker solution to be a weakly efficient solution.

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