scholarly journals On connectedness of the set of efficient solutions for generalized systems

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2413-2423
Author(s):  
M. Rahimi ◽  
A.P. Farajzadeh ◽  
S.M. Vaezpour
Keyword(s):  
Efficient Solutions ◽  
Density Theorem ◽  
Generalized System ◽  
Generalized Systems ◽  
Proper Efficient Solutions

In this paper, we first give a density theorem. We will see that, under some suitable conditions, the set of positive proper efficient solutions is dense in the set of the efficient solutions. Finally, we discuss about the connectedness for the set of the efficient solutions of a generalized system.

scholarly journals A notion of local proper efficiency in the Borwein sense in vector optimisation

2003 ◽  
Vol 45 (1) ◽  
pp. 75-89 ◽  
Author(s):  
B. Jiménez ◽  
V. Novo
Keyword(s):  
Efficient Solutions ◽  
Proper Efficiency ◽  
Proper Solution ◽  
Sufficient Condition ◽  
Strict Efficiency ◽  
Proper Efficient Solutions

AbstractIn this paper we define two types of proper efficient solutions in the Borwein sense for vector optimisation problems and we compare them with the notions of local Borwein, Ishizuka-Tuan, Kuhn-Tucker and strict efficiency. A sufficient condition for a proper solution is also proved.

scholarly journals Synchronization of Two Self-Synchronous Vibrating Machines on an Isolation Frame

2011 ◽  
Vol 18 (1-2) ◽  
pp. 73-90 ◽  
Author(s):  
Chunyu Zhao ◽  
Qinghua Zhao ◽  
Zhaomin Gong ◽  
Bangchun Wen
Keyword(s):  
Electromagnetic Torque ◽  
Frequency Capture ◽  
Generalized System ◽  
Rigid Frame ◽  
Generalized Systems ◽  
Three Phase ◽  
Small Parameters ◽  
Angular Velocities ◽  
The Absolute ◽  
The Stability

This paper investigates synchronization of two self-synchronous vibrating machines on an isolation rigid frame. Using the modified average method of small parameters, we deduce the non-dimensional coupling differential equations of the disturbance parameters for the angular velocities of the four unbalanced rotors. Then the stability problem of synchronization for the four unbalanced rotors is converted into the stability problems of two generalized systems. One is the generalized system of the angular velocity disturbance parameters for the four unbalanced rotors, and the other is the generalized system of three phase disturbance parameters. The condition of implementing synchronization is that the torque of frequency capture between each pair of the unbalanced rotors on a vibrating machine is greater than the absolute values of the output electromagnetic torque difference between each pair of motors, and that the torque of frequency capture between the two vibrating machines is greater than the absolute value of the output electromagnetic torque difference between the two pairs of motors on the two vibrating machines. The stability condition of synchronization of the two vibrating machines is that the inertia coupling matrix is definite positive, and that all the eigenvalues for the generalized system of three phase disturbance parameters have negative real parts. Computer simulations are carried out to verify the results of the theoretical investigation.

Strongly Proper Efficient Solutions: Efficient Solutions with Bounded Trade-Offs

2015 ◽  
Vol 168 (3) ◽  
pp. 864-883 ◽  
Author(s):  
Kazhal Khaledian ◽  
Esmaile Khorram ◽  
Majid Soleimani-damaneh
Keyword(s):  
Efficient Solutions ◽  
Trade Offs ◽  
Proper Efficient Solutions
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