An efficient inertial projection-based algorithm for constrained nonlinear pseudo-monotone equations and its application to logistic regression problems

The problem of solving nonlinear pseudo-monotone equations with convex constraints is studied in this paper. To solve this problem, an adaptive hyperplane projection method is proposed. At each iteration, a diagonal Barzilai–Borwein method is used to construct search direction. For the hyperplane projection step, an extrapolation step is applied by using a nonmonotone line search technique. In addition, an inertial technique is applied for possible acceleration of this new algorithm. Under the assumptions that the underlying map is continuous and the solution set is nonempty, the proposed new algorithm is globally convergent. Moreover, if the Lipschitz continuity condition and the local error bound condition are also satisfied, then the new algorithm has a local linear convergence rate. Numerical experiments are reported to show the efficiency of the proposed method.