An interactive algorithm for nonlinear vector optimization

1990 ◽  
Vol 22 (1) ◽  
pp. 147-151 ◽  
Author(s):  
Siegfried Helbig
Keyword(s):  
Vector Optimization ◽  
Interactive Algorithm ◽  
Nonlinear Vector Optimization ◽  
Nonlinear Vector

AN η-APPROXIMATION APPROACH IN NONLINEAR VECTOR OPTIMIZATION WITH UNIVEX FUNCTIONS

2006 ◽  
Vol 23 (04) ◽  
pp. 525-542 ◽  
Author(s):  
TADEUSZ ANTCZAK
Keyword(s):  
Programming Problem ◽  
Vector Optimization ◽  
Optimization Problem ◽  
Multiobjective Programming ◽  
Sufficient Conditions ◽  
Vector Optimization Problem ◽  
Approximation Approach ◽  
Nonlinear Vector Optimization ◽  
Multiobjective Programming Problem ◽  
Nonlinear Vector

In this paper, the so-called η-approximation approach is used to obtain the sufficient conditions for a nonlinear multiobjective programming problem with univex functions with respect to the same function η. In this method, an equivalent η-approximated vector optimization problem is constructed by a modification of both the objective and the constraint functions in the original multiobjective programming problem at the given feasible point. Moreover, to find the optimal solutions of the original multiobjective problem, it sufficies to solve its associated η-approximated vector optimization problem. Finally, the description of the η-approximation algorithm for solving a nonlinear multiobjective programming problem involving univex functions is presented.

Modification of Fuzzy c-Means Method Using a Nonlinear Vector Criterion

2010 ◽  
Vol 42 (12) ◽  
pp. 13-21
Author(s):  
Anatoliy F. Bulat ◽  
Elena M. Kiseleva ◽  
Sergey A. Pichugov ◽  
Oleg B. Blyuss
Keyword(s):  
Vector Criterion ◽  
Fuzzy C Means ◽  
Nonlinear Vector
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