On the degeneracy subgraph of Lemke`s algorithm and an anticycling rule
Let V be the set of almost complementary basic feasible solutions generated by Lemke`s complementary pivot algorithm and let A be the set of pairs (x, y) where x, y {element_of} V are adjacent. It is known that under the standard assumption of nondegeneracy the degree of any node of the graph G = (V, A) is at most 2. However when degenerate almost complementary basic feasible solutions are generated by the algorithm more than one almost complementary basis may correspond to the same degenerate solution and the degree of a node of the corresponding graph may be more than 2. In this paper we introduce the graph G{sub c}{sup +} = (N, E) where N is the set of almost complementary bases or tableaux associated with the linear complementarity problem, given the matrix M and the vector q, and E is the set of almost complementary bases (tableaux) in N such that there is a positive complementary pivot transformation from one tableau to the other of a pair. We study the structure of this graph and study an anticycling rule.
- OSTI ID:
- 36291
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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