Necessary Optimality Conditions for Bilevel Optimization Problems Using Convexificators

2006 ◽  
Vol 34 (4) ◽  
pp. 535-549 ◽  
Author(s):  
H. Babahadda ◽  
N. Gadhi
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Bilevel Optimization

scholarly journals Minimum Principle-Type Necessary Optimality Conditions in Scalar and Vector Optimization. An Account

2017 ◽  
Vol 9 (4) ◽  
pp. 168
Author(s):  
Giorgio Giorgi
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Minimum Principle ◽  
Necessary Optimality Conditions ◽  
Equality Constraints ◽  
Vector Optimization Problems ◽  
Scalar Optimization ◽  
Scalar And Vector Optimization

We take into condideration necessary optimality conditions of minimum principle-type, that is for optimization problems having, besides the usual inequality and/or equality constraints, a set constraint. The first part pf the paper is concerned with scalar optimization problems; the second part of the paper deals with vector optimization problems.

Optimality Principles for Fuzzy Dual Uncertain Systems

2018 ◽  
pp. 47-72
Author(s):  
Félix Mora-Camino ◽  
Hakim Bouadi ◽  
Roger Marcelin Faye ◽  
Lunlong Zhong
Keyword(s):  
Optimality Conditions ◽  
Calculus Of Variations ◽  
Optimization Problems ◽  
Lagrange Equation ◽  
Necessary Optimality Conditions ◽  
Continuous System ◽  
Propagation Of Uncertainty ◽  
Performance Indexes ◽  
Definition Of ◽  
Optimality Principles

This chapter considers the extension of the calculus of variations to the optimization of a class of fuzzy systems where the uncertainty of variables and parameters is represented by symmetrical triangular membership functions. The concept of fuzzy dual numbers is introduced, and the consideration of the necessary differentiability conditions for functions of dual variables leads to the definition of fuzzy dual functions. It is shown that when this formalism is adopted to represent performance indexes for uncertain optimization problems, the calculus of variations can be used to establish necessary optimality conditions as an extension to this case of the Euler-Lagrange equation. Then the chapter discusses the propagation of uncertainty when the fuzzy dual formalism is adopted for the state representation of a time continuous system. This leads to the formulation of a fuzzy dual optimization problem for which necessary optimality conditions, corresponding to an extension of Pontryagine's optimality principle, are established.

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