Strict Efficiency in Set-Valued Optimization

2009 ◽  
Vol 48 (2) ◽  
pp. 881-908 ◽  
Author(s):  
Fabián Flores-Bazán ◽  
Bienvenido Jiménez
Keyword(s):  
Strict Efficiency

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 Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Xiaohong Hu ◽  
Zhimiao Fang ◽  
Yunxuan Xiong
Keyword(s):  
Saddle Point ◽  
Vector Optimization ◽  
Optimization Problem ◽  
Efficient Solutions ◽  
Vector Optimization Problem ◽  
Well Posedness ◽  
Scalar Problem ◽  
New Type ◽  
Strict Efficiency ◽  
Multiplier Theorems

The concept of the well posedness for a special scalar problem is linked with strictly efficient solutions of vector optimization problem involving nearly convexlike set-valued maps. Two scalarization theorems and two Lagrange multiplier theorems for strict efficiency in vector optimization involving nearly convexlike set-valued maps are established. A dual is proposed and duality results are obtained in terms of strictly efficient solutions. A new type of saddle point, called strict saddle point, of an appropriate set-valued Lagrange map is introduced and is used to characterize strict efficiency.

scholarly journals PLOT, STORY, COMPOSITION IN THE EMOTIVE TEXT OF POETRY

2018 ◽  
Vol 63 (3) ◽  
pp. 355-365
Author(s):  
S. V. Коlyadko
Keyword(s):  
Effect Relationship ◽  
Cause And Effect ◽  
Poetic Text ◽  
Strict Efficiency ◽  
Emotional Events ◽  
Poetic Work ◽  
The Way ◽  
Verse Structure

In the article there is an attempt to enter emotion in the structure of work, namely to look at its action at the level of plot and composition. It becomes firmly established that an emotion is just the way to create a plot. The poetic work consists of emotional events, each of which has its own dominant emotion. Motion of these emotions forms composition of a plot. A thesis is grounded that emotional events, incorporated by a general emotion, express certain emotive topics that predetermine as a whole the development of a plot. Emotions are a part of poetic text, emotions determine its emotionality and serve as material for revealing of the emotions in a plot. It is noted that Maksim Tank gives preference to his anecdotal works where a little story is present and where elements of plot – emotive topics – are linked by a cause-and-effect relationship. But Yauheniya Yanishchyts avoids a strict efficiency of verse structure, she prefers to leave emotions and feelings free. 

scholarly journals The Strictly Efficient Subgradient of Set-Valued Optimisation

2007 ◽  
Vol 75 (3) ◽  
pp. 361-371 ◽  
Author(s):  
Taiyong Li ◽  
Yihong Xu
Keyword(s):  
Optimality Conditions ◽  
Lagrange Multipliers ◽  
Efficient Point ◽  
Set Valued Mapping ◽  
Strict Efficiency

The subgradient, under strict efficiency, of a set-valued mapping is developed, and the existence of the subgradient is proved. Optimality conditions in terms of Lagrange multipliers for a strictly efficient point are established in the general case and in the case with ic-cone-convexlike data.

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