Duality theory in Atanassov’s intuitionistic fuzzy mathematical programming problems: Optimistic, pessimistic and mixed approaches

2019 ◽  
Vol 296 (1-2) ◽  
pp. 667-706
Author(s):  
Vishnu Singh ◽  
Shiv Prasad Yadav ◽  
Sujeet Kumar Singh
Keyword(s):  
Mathematical Programming ◽  
Duality Theory ◽  
Fuzzy Mathematical Programming ◽  
Intuitionistic Fuzzy ◽  
Mathematical Programming Problems

Multi-Objective Generation Scheduling Using Genetic-Based Fuzzy Mathematical Programming Technique

2014 ◽  
pp. 450-474 ◽  
Author(s):  
Abdellah Derghal ◽  
Noureddine Goléa
Keyword(s):  
Mathematical Programming ◽  
Optimal Power Flow ◽  
Optimal Solution ◽  
Fuzzy Mathematical Programming ◽  
Programming Technique ◽  
Solution Approach ◽  
Physical Constraints ◽  
Multi Objective ◽  
Generation Scheduling ◽  
Mathematical Programming Problems

This chapter presents a solution for multi-objective Optimal Power Flow (OPF) problem via a genetic fuzzy formulation algorithm (GA-FMOPF). The OPF problem is formulated as a multiple objective problem subject to physical constraints. The objectives and constraints are modelled as fuzzy mathematical programming problems involving the minimization of the objective function with fuzzy parameters and uncertainties in set of constraints. So the method is capable of representing practical situations in power system operation where the limits on specific variables are soft and the small violations of these limits may be tolerable. Then, genetic algorithm is used in order to seek a feasible optimal solution to the environmental/economic dispatch problem. Illustrative examples are given to clarify the proposed method developed in this manuscript and the performance of this solution approach is evaluated by comparing its results with that of their existing methods.

Characterizations of optimality for continuous convex mathematical programs. Part I. Linear constraints

1979 ◽  
Vol 21 (1) ◽  
pp. 37-44 ◽  
Author(s):  
C. H. Scott ◽  
T. R. Jefferson
Keyword(s):  
Mathematical Programming ◽  
Duality Theory ◽  
Linear Constraints ◽  
Lagrangian Formalism ◽  
Symmetric Duality ◽  
Mathematical Programs ◽  
Convex Functionals ◽  
Mathematical Programming Problems

AbstractRecently we have developed a completely symmetric duality theory for mathematical programming problems involving convex functionals. Here we set our theory within the framework of a Lagrangian formalism which is significantly different to the conventional Lagrangian. This allows various new characterizations of optimality.

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