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Optimality conditions for weak efficiency to vector optimization problems with composed convex functions

100%
Boţ R., Hodrea I., Wanka G.
Open Mathematics
|
2008
|
tom 6
|
nr 3
453-468
EN
We consider a convex optimization problem with a vector valued function as objective function and convex cone inequality constraints. We suppose that each entry of the objective function is the composition of some convex functions. Our aim is to provide necessary and sufficient conditions for the weakly efficient solutions of this vector problem. Moreover, a multiobjective dual treatment is given and weak and strong duality assertions are proved.
2
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Comparison between different duals in multiobjective fractional programming

100%
Boţ R., Chares R., Wanka G.
Open Mathematics
|
2007
|
tom 5
|
nr 3
452-469
EN
The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets.
3
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Nature–inspired metaheuristic algorithms to find near–OGR sequences for WDM channel allocation and their performance comparison

100%
Bansal S., Gupta N., Singh A. K.
Open Mathematics
|
2017
|
tom 15
|
nr 1
520-547
EN
Nowadays, nature–inspired metaheuristic algorithms are most powerful optimizing algorithms for solving the NP–complete problems. This paper proposes three approaches to find near–optimal Golomb ruler sequences based on nature–inspired algorithms in a reasonable time. The optimal Golomb ruler (OGR) sequences found their application in channel–allocation method that allows suppression of the crosstalk due to four–wave mixing in optical wavelength division multiplexing systems. The simulation results conclude that the proposed nature–inspired metaheuristic optimization algorithms are superior to the existing conventional and nature–inspired algorithms to find near–OGRs in terms of ruler length, total optical channel bandwidth, computation time, and computational complexity. Based on the simulation results, the performance of proposed different nature–inspired metaheuristic algorithms are being compared by using statistical tests. The statistical test results conclude the superiority of the proposed nature–inspired optimization algorithms.
4
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An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems

84%
Petruşel A., Yao J.-C.
Open Mathematics
|
2009
|
tom 7
|
nr 2
335-347
EN
In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.
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