Recent studies on the kernel function-based primal-dual interior-point algorithms indicate that a kernel function not only represents a measure of the distance between the iteration and the central path, but also plays a critical role in improving the computational complexity of an...

Kernel functions play an important role in interior point methods (IPMs) for solving linear optimization (LO) problems to define a new search direction. In this paper, we consider primal-dual algorithms for solving Semidefinite Optimization (SDO) problems based on a new class of kernel functions...

A new predictor--corrector interior point algorithm for solving monotone linear complementarity problems (LCP) is proposed, and it is shown to be superlinearly convergent with at least order 1.5, even if the LCP has no strictly complementary solution. Unlike Mizuno's recent algorithm (Mizuno,...

In this paper a symmetric primal-dual transformation for positive semidefinite programming is proposed. For standard SDP problems, after this symmetric transformation the primal variables and the dual slacks become identical. In the context of linear programming, existence of such a primal-dual...