Necessary conditions for a domain optimization problem with various constraints

1996 ◽  
Vol 90 (2) ◽  
pp. 243-255 ◽  
Author(s):  
S. A. Belov ◽  
S. N. Sluguin
Keyword(s):  
Optimization Problem ◽  
Necessary Conditions ◽  
Domain Optimization

scholarly journals Necessary conditions for optimal control of elliptic systems

2000 ◽  
Vol 41 (4) ◽  
pp. 542-567 ◽  
Author(s):  
Hang Gao ◽  
Xunjing Li
Keyword(s):  
Optimal Control ◽  
Elliptic Equation ◽  
Optimization Problem ◽  
Necessary Conditions ◽  
Elliptic Systems ◽  
Semilinear Elliptic Equation ◽  
Optimal Domain ◽  
Domain Optimization ◽  
Semilinear Elliptic

AbstractIn this paper, we consider the system governed via the coefficients of a semilinear elliptic equation and give the necessary conditions for optimal control. Furthermore, we obtain the necessary conditions for an optimal domain in a domain optimization problem.

scholarly journals Optimality conditions via scalarization for approximate quasi efficiency in multiobjective optimization

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 671-680 ◽  
Author(s):  
Mehrdad Ghaznavi
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Original Problem ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Multiobjective Optimization Problem ◽  
Alternative Theorem ◽  
Convexity Assumptions ◽  
Interesting Area

Approximate problems that scalarize and approximate a given multiobjective optimization problem (MOP) became an important and interesting area of research, given that, in general, are simpler and have weaker existence requirements than the original problem. Recently, necessary conditions for approximation of several types of efficiency for MOPs have been obtained through the use of an alternative theorem. In this paper, we use these results in order to extend them to sufficient conditions for approximate quasi (weak, proper) efficiency. For this, we use two scalarization techniques of Tchebycheff type. All the provided results are established without convexity assumptions.

Optimality Conditions for Pareto-Optimal Solutions

2016 ◽  
Vol 685 ◽  
pp. 142-147
Author(s):  
Vladimir Gorbunov ◽  
Elena Sinyukova
Keyword(s):  
Multicriteria Optimization ◽  
Optimization Problem ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Sufficient Conditions ◽  
Optimal Solutions ◽  
Main Criterion ◽  
Linear Optimization Problems ◽  
Necessary And Sufficient

In this paper the authors describe necessary conditions of optimality for continuous multicriteria optimization problems. It is proved that the existence of effective solutions requires that the gradients of individual criteria were linearly dependent. The set of solutions is given by system of equations. It is shown that for finding necessary and sufficient conditions for multicriteria optimization problems, it is necessary to switch to the single-criterion optimization problem with the objective function, which is the convolution of individual criteria. These results are consistent with non-linear optimization problems with equality constraints. An example can be the study of optimal solutions obtained by the method of the main criterion for Pareto optimality.

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