Linear complementarity problem

Kuhn-Tucker conditions and reduces the quadratic programming problem to what is referred to as a linear complementarity problem. 

Written in this form, (74)-(76) are an example of a linear complementarity problem, which also has applications in game theory. In this context, (76) is referred to as the complementarity condition, and all Wi, Zi pairs are said to be complementary variables. A method for finding a solution to this system is the complementary pivoting algorithm credited to Lemke (1968). Under certain assumptions on the matrix M, the algorithm determines a solution or finds a direction indicating unboundedness in a finite number of iterations. 

Ko HY, Kwak BM. Contact analysis of mechanically fastened joints in composite laminates by linear complementarity problem formulation. Compos Struct 1998 ... 

BRANDT A., C. W. CRYER (1983), "Multigrid Algorithms for the Solution of Linear Complementarity Problems Arising from Free Boundary Problems". SIAM. J. Scl. Stat. Comput. vol 4, No. 4 pp 655-684. 

Since pn is a linear function of An these conditions form a linear complementarity problem, which can be solved by using Simplex-like algorithms as the one given in [Sey93, GP92]. This has to be done at any time-point where the necessary conditions for structure changing (6.5.6), (6.5.7) become active. 

Similarly, sufficient conditions for a stiction phase and the instance before/after stiction can be formulated. These conditions can again be reformulated as linear complementarity problem by splitting the values into their positive and negative part to get rid of the absolute values [GP92]. 

When the rod is in contact with the surface we have N >0 and y, = 0. On the other hand, when the rod brakes contact we have N = 0 and > 0. This situation can be represented as a linear complementarity problem [52, 96] which is written compactly as... 

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