Constructions of Generalized Differentiation

2018 ◽  
pp. 1-66 ◽  
Author(s):  
Boris S. Mordukhovich
Keyword(s):  
Generalized Differentiation

NECESSARY OPTIMALITY CONDITIONS FOR SUPER MINIMIZERS IN STRUCTURAL PROBLEMS OF MULTIOBJECTIVE OPTIMIZATION

2009 ◽  
Vol 02 (02) ◽  
pp. 321-358 ◽  
Author(s):  
Lu-Chuan Zeng
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Variational Analysis ◽  
Necessary Conditions ◽  
Necessary Optimality Conditions ◽  
Generalized Differentiation ◽  
Infinite Dimensional ◽  
Structural Problems ◽  
Constrained Problems ◽  
Finite Dimensional

The primary goal of this paper is to study the so-called super minimizers of the sum F1 + F2 related to the concept of super efficiency in constrained problems of multiobjective optimization, where each cost mapping Fi is generally set-valued for i = 1, 2. We will derive necessary conditions (of the subdifferential type) for super minimizers of the sum F1 + F2 on the basis of advanced tools of variational analysis and generalized differentiation that are new in both finite-dimensional and infinite-dimensional settings for problems with single-valued and set-valued objectives.

Gel’fond-Leont’ev generalized differentiation operators in spaces of type S

2013 ◽  
Vol 54 (3) ◽  
pp. 446-458 ◽  
Author(s):  
V. V. Gorodetsky ◽  
O. V. Martynyuk
Keyword(s):  
Generalized Differentiation
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