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A polynomial-time algorithm for linear optimization based on a new kernel function with trigonometric barrier term

Kheirfam B. (Department of Mathematics Azarbaijan Shahid Madani University Tabriz, Iran)
Moslemi M. (Department of Mathematics Azarbaijan Shahid Madani University Tabriz, Iran)

In this paper, we propose a large-update interior-point algorithm for linear optimization based on a new kernel function. New search directions and proximity measure are defined based on this kernel function. We show that if a strictly feasible starting point is available, then the new algorithm has O(3/4log n/ε) iteration complexity.

Keywords: Kernel function, interior-point algorithm, linear optimization, polynomial complexity, primal-dual method