Mathematics of Operations Research
The largest step path following algorithm for monotone linear complementarity problems
Mathematical Programming: Series A and B
Fast convergence of the simplified largest step path following algorithm
Mathematical Programming: Series A and B - Special issue: interior point methods in theory and practice
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
A New Efficient Large-Update Primal-Dual Interior-Point Method Based on a Finite Barrier
SIAM Journal on Optimization
Global convergence enhancement of classical linesearch interior point methods for MCPs
Journal of Computational and Applied Mathematics
SIAM Journal on Optimization
Journal of Computational and Applied Mathematics
A new large-update interior point algorithm for P*(κ) linear complementarity problems
Journal of Computational and Applied Mathematics
A polynomial-time algorithm for linear optimization based on a new class of kernel functions
Journal of Computational and Applied Mathematics
A matrix-splitting method for symmetric affine second-order cone complementarity problems
Journal of Computational and Applied Mathematics
Using vector divisions in solving the linear complementarity problem
Journal of Computational and Applied Mathematics
A full-Newton step feasible interior-point algorithm for P*(κ)-linear complementarity problems
Journal of Global Optimization
Hi-index | 7.30 |
In this paper a class of polynomial interior-point algorithms for P"*(@k) horizontal linear complementarity problem based on a new parametric kernel function, with parameters p@?[0,1] and @s=1, are presented. The proposed parametric kernel function is not exponentially convex and also not strongly convex like the usual kernel functions, and has a finite value at the boundary of the feasible region. It is used both for determining the search directions and for measuring the distance between the given iterate and the @m-center for the algorithm. The currently best known iteration bounds for the algorithm with large- and small-update methods are derived, namely, O((1+2@k)nlognlogn@e) and O((1+2@k)nlogn@e), respectively, which reduce the gap between the practical behavior of the algorithms and their theoretical performance results. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p,@s and @q.