• 대한수학회논문집
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• 제31권4호
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• pp.879-893
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• 2016

In this paper, we introduce three subgradient extragradient algorithms for solving pseudomonotone equilibrium problems. The paper originates from the subgradient extragradient algorithm for variational inequalities and the extragradient method for pseudomonotone equilibrium problems in which we have to solve two optimization programs onto feasible set. The main idea of the proposed algorithms is that at every iterative step, we have replaced the second optimization program by that one on a specific half-space which can be performed more easily. The weakly and strongly convergent theorems are established under widely used assumptions for bifunctions.

• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.83-99
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• 2019

In this paper, we introduce a hybrid subgradient method for finding an element common to both the solution set of a class of pseudomonotone equilibrium problems, and the set of fixed points of a finite family of ${\kappa}$-strictly presudononspreading mappings in a real Hilbert space. We establish some weak and strong convergence theorems of the sequences generated by our iterative method under some suitable conditions. These convergence theorems are investigated without the Lipschitz condition for bifunctions. Our results complement many known recent results in the literature.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제9권1호
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• pp.149-168
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• 2015

In cognitive radio networks (CRNs), hybrid overlay and underlay sharing transmission mode is an effective technique for improving the efficiency of radio spectrum. Unlike existing works in the literature, where only one secondary user (SU) uses overlay and underlay modes, the different transmission modes should be allocated to different SUs, according to their different quality of services (QoS), to achieve the maximal efficiency of radio spectrum. However, hybrid sharing mode allocation for heterogeneous services is still a challenge in CRNs. In this paper, we propose a new resource allocation method for hybrid sharing transmission mode of overlay and underlay (HySOU), to achieve more potential resources for SUs to access the spectrum without interfering with the primary users. We formulate the HySOU resource allocation as a mixed-integer programming problem to optimize the total system throughput, satisfying heterogeneous QoS. To decrease the algorithm complexity, we divide the problem into two sub-problems: subchannel allocation and power allocation. Cutset is used to achieve the optimal subchannel allocation, and the optimal power allocation is obtained by Lagrangian dual function decomposition and subgradient algorithm. Simulation results show that the proposed algorithm further improves spectrum utilization with a simultaneous fairness guarantee, and the achieved HySOU diversity gain is a satisfactory improvement.