We suggest and analyze a new explicit projection method for solving the system under some more general conditions.
This alternative formulation enable us to suggest and analyze an explicit projection method for solving system (2.1).
By utilizing Lemma 4.1, we suggest and analyze the following explicit projection iterative methods for solving problem (11).
We establish the equivalence between the new system of general nonconvex variational inequalities and the fixed point problems to analyze an explicit projection method for solving this system.
Furthermore, the computation workload of the present explicit projection method is much less than the implicit algorithm in [5] at each iteration step.
This projection scheme basically consists in storing the explicit projection matrix (tilde{P}) with a Compressed Sparse Row (CSR) format [17], where LUT J corresponds to "col_ind," LUT (mathrm {Pos}) corresponds to "row_ptr," and matrix W contains the values.
If g = h = I, K r = K, and T1, T2 : K → K are two univariate nonlinear operators, then Algorithm 3.1 reduces to the following explicit projection method for solving the system of variational inequalities (2.4): Algorithm 3.3.
By using the obtained equivalences, we have proved the existence of a unique solution for RNVI (11) and suggested and analyzed some explicit projection iterative methods for solving RNVI (11).
This alternative formula enables us to suggest and analyze a two-step explicit projection method for solving system (1.6), and this is the main motivation of our next result.
If β n = 1, K r = K, then Algorithm 3.1 reduces to the following explicit projection method for solving the system of variational inequalities (2.3), which is mainly due to Noor and Noor [14]: Algorithm 3.2.
