On the Alass of Complementary Cones and Lemke’s Algorithm

1972 ◽  
Vol 23 (1) ◽  
pp. 46-60 ◽  
Author(s):  
Romesh Saigal
Keyword(s):  
Lemke's Algorithm ◽  
Complementary Cones

Computing Economic Equilibria on Affine Networks with Lemke's Algorithm

1979 ◽  
Vol 4 (3) ◽  
pp. 209-214 ◽  
Author(s):  
Richard Asmuth ◽  
B. Curtis Eaves ◽  
Elmor L. Peterson
Keyword(s):  
Economic Equilibria ◽  
Lemke's Algorithm

Proper, reflecting and absorbing facts of complementary cones

1985 ◽  
Vol 31 (1) ◽  
pp. 106-117 ◽  
Author(s):  
Romesh Saigal ◽  
Richard E. Stone
Keyword(s):  
Complementary Cones

scholarly journals Complementary cones in dual Banach spaces

1974 ◽  
Vol 18 (4) ◽  
pp. 657-668 ◽  
Author(s):  
Leonard Asimow
Keyword(s):  
Banach Spaces ◽  
Complementary Cones

On the average speed of Lemke's algorithm for quadratic programming

1986 ◽  
Vol 35 (2) ◽  
pp. 236-246 ◽  
Author(s):  
Yieh-Hei Wan
Keyword(s):  
Quadratic Programming ◽  
Average Speed ◽  
Lemke's Algorithm

On strongly degenerate complementary cones and solution rays

1989 ◽  
Vol 44 (1-3) ◽  
pp. 77-83 ◽  
Author(s):  
N. Eagambaram ◽  
S. R. Mohan
Keyword(s):  
Complementary Cones ◽  
Strongly Degenerate

Degenerate complementary cones induced by aK 0-matrix

1981 ◽  
Vol 20 (1) ◽  
pp. 103-109 ◽  
Author(s):  
S. R. Mohan
Keyword(s):  
Complementary Cones

ON FULLY SEMIMONOTONE MATRICES

2013 ◽  
Vol 15 (04) ◽  
pp. 1340036 ◽  
Author(s):  
G. S. R. MURTHY ◽  
T. PARTHASARATHY ◽  
R. SRIDHAR
Keyword(s):  
Linear Complementarity Problem ◽  
Operations Research ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Special Structure ◽  
Stanford University ◽  
Complementary Cones ◽  
Math Program ◽  
Special Case

The class of fully semimonotone matrices is well known in the study of the linear complementarity problem. Stone [(1981) Ph.D. thesis, Dept. of Operations Research, Stanford University, Stanford, CA] introduced this class and conjectured that the principal minors of any fully semimonotone Q0-matrix are non-negative. While the problem is still open, Murthy and Parthasarathy [(1998) Math. Program.82, 401–411] introduced the concept of incidence using which they proved that the principal minors of any matrix in the class of fully copositive Q0-matrices, a subclass of fully semimonotone Q0-matrices, are non-negative. In this paper, we study some properties of fully semimonotone matrices in connection with incidence. The main result of the paper shows that Stone's conjecture is true in the special case where the complementary cones have no partial incidence. We also present an interesting characterization of Q0 for matrices with a special structure. This result is very useful in checking whether a given matrix belongs to Q0 provided it has the special structure. Several examples are discussed in connection with incidence and Q0 property.

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