Abstract: In this article, we shall discuss the velocity of the collective motion of sedimentation when the concentration of clay particles is very high. We believe that the problem of the so-called velocity of the collective motion of sedimentation is not a real problem of sedimentation in physical nature, but it is a problem of filtration in the porous medium which is composed of colloidal clusters. That is to say, those clusters consist of water and clay particles.It is a problem of the water passing through the porous medium. Based upon this consideration, we put down the mathematical expression of the velocity of the collective motion of sedimentation. In comparing with the theoretical curves with the experimental data of the Institute of Hydraulic Research, of the Yellow River Conservancy Commission, we get congruous results.

Key words: min-max problem, constrained optimization, penalty function