On Minty Variational Principle for Nonsmooth Interval-Valued Multiobjective Programming Problems

2021 ◽  
pp. 265-282
Author(s):  
Balendu Bhooshan Upadhyay ◽  
Priyanka Mishra
Keyword(s):  
Variational Principle ◽  
Multiobjective Programming ◽  
Multiobjective Programming Problems ◽  
Interval Valued

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.

Sign in / Sign up

Export Citation Format

Share Document