Monotonicity of Mangasarian's iterative algorithm for generalized linear complementarity problems (Q582015)

Discretization of the Hamilton-Jacobi-Bellman equations of control theory leads to a generalized linear complementary problem (GLCP) of the form \(A_ jx+q_ j\geq 0,\) \(j=1,2,...,m,\) \(\min \{A_ jx+q_ j*\quad j=1,2,...,m\}=0.\) The author extend \textit{O. L. Mangasarian}'s iterative algorithm [J. Optimization Theory Appl. 22, 465-485 (1977; Zbl 0341.65049)] for linear complementarity problems to GLCP. He imposes some additional conditions on the initial point \(x_ 0\) in order to get the monotonicity of the subsequent iterates. As a consequence of the monotonicity the convergence of the method is obtained. The algorithm has been tested on a singular stochastic control problem.