372 research outputs found
Enumeration of PLCP-orientations of the 4-cube
The linear complementarity problem (LCP) provides a unified approach to many
problems such as linear programs, convex quadratic programs, and bimatrix
games. The general LCP is known to be NP-hard, but there are some promising
results that suggest the possibility that the LCP with a P-matrix (PLCP) may be
polynomial-time solvable. However, no polynomial-time algorithm for the PLCP
has been found yet and the computational complexity of the PLCP remains open.
Simple principal pivoting (SPP) algorithms, also known as Bard-type algorithms,
are candidates for polynomial-time algorithms for the PLCP. In 1978, Stickney
and Watson interpreted SPP algorithms as a family of algorithms that seek the
sink of unique-sink orientations of -cubes. They performed the enumeration
of the arising orientations of the -cube, hereafter called
PLCP-orientations. In this paper, we present the enumeration of
PLCP-orientations of the -cube.The enumeration is done via construction of
oriented matroids generalizing P-matrices and realizability classification of
oriented matroids.Some insights obtained in the computational experiments are
presented as well
Symmetric confidence regions and confidence intervals for normal map formulations of stochastic variational inequalities
Stochastic variational inequalities (SVI) model a large class of equilibrium
problems subject to data uncertainty, and are closely related to stochastic
optimization problems. The SVI solution is usually estimated by a solution to a
sample average approximation (SAA) problem. This paper considers the normal map
formulation of an SVI, and proposes a method to build asymptotically exact
confidence regions and confidence intervals for the solution of the normal map
formulation, based on the asymptotic distribution of SAA solutions. The
confidence regions are single ellipsoids with high probability. We also discuss
the computation of simultaneous and individual confidence intervals
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