Abstract
The convergence of Rosen's gradient projection method is a long-standing problem in nonlinear programming. Recently, Zhang[27] proved that it is convergent in the 3-dimensional space; Du and Zhang[5] proved its convergence inn-dimensional space under a restriction on a paramater in Rosen's method. In this paper, we propose a linearly algebraic conjecture which can yield the convergence of Rosen's method without the restriction. By verifying this conjecture for some special cases, we prove that Rosen's method is convergent in 4-dimensional space.
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