Tibor Illés

A Strongly Polynomial Rounding Procedure Yielding a Maximally Complementary Solution for

We deal with linear complementarity problems (LCPs) with

P_*(\kappa)

P_*(\kappa)

Linear Complementarity Problems

matrices. First we establish the convergence rate of the complementary variables along the central path. The central path is parameterized by the barrier parameter

Theorems of the alternative and optimality conditions for convexlike and general convexlike programming

\mu

Pivot versus interior point methods: pros and cons

, as usual. Our elementary proof reproduces the known result that the variables on or close to the central path fall apart in three classes in which these variables are

A polynomial path-following interior point algorithm for general linear complementarity problems

{\cal O}(1), {\cal O}(\mu),

New criss-cross type algorithms for linear complementarity problems with sufficient matrices

and

Three-dimensional principal component analysis employed for the study of the β-glucosidase production of Lentinus edodes strains

{\cal O}(\sqrt{\mu})

Application of nonlinear optimization to reactor core fuel reloading

, respectively. The constants hidden in these bounds are expressed in or bounded by the input data. All this is preparation for our main result: a strongly polynomial rounding procedure. Given a point with sufficiently small complementarity gap and which is close enough to the central path, the rounding procedure produces a maximally complementary solution in at most

The s-monotone index selection rules for pivot algorithms of linear programming

{\cal O} (n^3)