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Recently, Mangasarian [18, 19] has discussed the idea of solving certain classes of linear complementarity problems as linear programs. The present paper (1) demonstrates how these complementarity problems are related to the theory of... more
Recently, Mangasarian [18, 19] has discussed the idea of solving certain classes of linear complementarity problems as linear programs. The present paper (1) demonstrates how these complementarity problems are related to the theory of polyhedral sets having least elements and (2) discusses the question of whether the linear programming approach can be recommended for solving them.
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For a fixedm × n matrixA, we consider the family of polyhedral setsXb ={x|Ax = b}, b ? Rm, and prove a theorem characterizing, in terms ofA, the circumstances under which every nonemptyXb has a least element. In the special case whereA... more
For a fixedm × n matrixA, we consider the family of polyhedral setsXb ={x|Ax = b}, b ? Rm, and prove a theorem characterizing, in terms ofA, the circumstances under which every nonemptyXb has a least element. In the special case whereA contains all the rows of ann × n identity matrix, the conditions are equivalent toAT being Leontief. Among
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... Personal Author(s) : Cottle,Richard W. ; Dantzig,George B. Report Date : APR 1967. Pagination or Media Count : 39. Abstract : Problems of the form: Find w and z satisfying w = q + Mz, w = or > 0, z = or... more
... Personal Author(s) : Cottle,Richard W. ; Dantzig,George B. Report Date : APR 1967. Pagination or Media Count : 39. Abstract : Problems of the form: Find w and z satisfying w = q + Mz, w = or > 0, z = or > 0, zw = 0 play a fundamental role in mathematical programming. ...
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In this paper, some existence results for a nonlinear complementarity problem involving a pseudo-monotone mapping over an arbitrary closed convex cone in a real Hilbert space are established. In particular, some known existence results... more
In this paper, some existence results for a nonlinear complementarity problem involving a pseudo-monotone mapping over an arbitrary closed convex cone in a real Hilbert space are established. In particular, some known existence results for a nonlinear complementarity problem in a finite-dimensional Hilbert space are generalized to an infinite-dimensional real Hilbert space. Applications to a class of nonlinear complementarity problems
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... Again, the nonsymmetric matrices 1 1 A = ( 9 9) with Det A = 0 and 1 4 B = (I 1 with Det B 0 illustrate that the theorem is not valid for nonsymmetric M. 4. DETERMINANTAL CRITERIA In [5] we briefly reviewed the determinantal... more
... Again, the nonsymmetric matrices 1 1 A = ( 9 9) with Det A = 0 and 1 4 B = (I 1 with Det B 0 illustrate that the theorem is not valid for nonsymmetric M. 4. DETERMINANTAL CRITERIA In [5] we briefly reviewed the determinantal copositivity test suggested by Motzkin [13; see also ...
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... Large, Structured Linear Complementarity Problems ... and t~ is the spectral radius of/3. We have performed numerical experiments on the problem described in Section 3 ... First, we compute q to correspond to the finite difference... more
... Large, Structured Linear Complementarity Problems ... and t~ is the spectral radius of/3. We have performed numerical experiments on the problem described in Section 3 ... First, we compute q to correspond to the finite difference equations for the journal bearing problem [6], [17]. ...
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Advanced Research Projects Agency (ARPA), 9 American Association for the Advancement of Science, 5 AMRC Papers, The, 26 Andersen, Gerald R., xi Andrews, George, 59 Anselone, Philip M., 54, 55, 63 Applied functional analysis, 57... more
Advanced Research Projects Agency (ARPA), 9 American Association for the Advancement of Science, 5 AMRC Papers, The, 26 Andersen, Gerald R., xi Andrews, George, 59 Anselone, Philip M., 54, 55, 63 Applied functional analysis, 57 Archimedes, 5 Areas of concentration, 18, 22, 31, 33, 38 Army High Performance Computing Research Center (AHPCRC), 66, 73, 74, 76 Army Map Service, 60 Army Mathematics Advisory Group (AMAG), 9 Army Mathematics Steering Committee (AMSC), 2, 9, 15, 71, 75 Askey, ...