Recently, Lawphongpanich and Yin (2010) proposed a Manifold Suboptimization algorithm for finding a "strongly stationary" solution to a Pareto-improving toll problem by solving a sequence of relaxed problems. This note shows that Lawphongpanich and Yin's algorithm may not always converges to satisfactory solutions. In this paper, we provide several examples to demonstrate that the manifold suboptimization algorithm is inefficient in solving mathematical programs with complementarity constraints (MPCC) under certain conditions. This note also offers some insights and directions to improve the manifold suboptimization problems in the application of solving bi-level programs.
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