Projected Subgradient Algorithms for Pseudomonotone Equilibrium Problems and Fixed Points of Pseudocontractive Operators

The projected subgradient algorithms can be considered as an improvement of the projected algorithms and the subgradient algorithms for the equilibrium problems of the class of monotone and Lipschitz continuous operators. In this paper, we present and analyze an iterative algorithm for finding a common element of the fixed point of pseudocontractive operators and the pseudomonotone equilibrium problem in Hilbert spaces. The suggested iterative algorithm is based on the projected method and subgradient method with a linearsearch technique. We show the strong convergence result for the iterative sequence generated by this algorithm. Some applications are also included. Our result improves and extends some existing results in the literature.

Distributed Optimal Maximum Rate Allocation based on Data Aggregation in Rechargeable Wireless Sensor Networks

<p class="0abstract"><span lang="EN-US">In Rechargeable Wireless Sensor Networks(R-WSNs), it is critical for data collection because a sensor has to operate in a very low and dynamic duty cycle owing to sporadic availability of energy. In this work, we propose a distribute maximum rate allocation based on data aggregation to compute an upper data generation rate by maximizing it as a linear programming problem. Subsequently, a dual problem by introducing Lagrange multipliers is constructed, and subgradient algorithms are used to solve it in a distributed manner. The resulting algorithms are guaranteed to converge to an optimal value with low computational complexity. Through extensive simulation and experiments, we demonstrate our algorithm is efficient to maximize data collection rate in rechargeable wireless sensor networks.</span></p>