We propose a primal-dual interior-point algorithm for linear optimisation based on a class of kernel functions which is eligible. New search directions and proximity measures are defined based on these functions. We derive the complexity bounds for large and small-update methods respectively. These are currently the best known complexity results for such methods.

In this paper, we present an interior-point algorithm for solving an optimization problem using the central path method. By an equivalent reformulation of the central path, we obtain a new search direction which targets at a small neighborhood of the central path. For a full-Newton step interior-point algorithm based on this search direction, the complexity bound of the algorithm is the best known for linear complementarity problem. For its numerical tests, some strategies are used and indicate that the algorithm is efficient.

In this paper, we present an interior point algorithm for solving an optimization problem using the central path method. By an equivalent reformulation of the central path, we obtain a new search direction which targets at a small neighborhood of the central path. For a full-Newton step interior-point algorithm based on this search direction, the complexity bound of the algorithm is the best known for linear complementarity problem. For its numerical tests some strategies are used and indicate that the algorithm is efficient.

In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we show that the worst-case iteration bound for our IPM is O(6(m+1)3m+42(m+1)Ψm+22(m+1)01θlognμ0ε)O(6(m+1)3m+42(m+1)Ψ0m+22(m+1)1θlog⁡nμ0ε), where m>4m>4.

In this paper we deal with the study of the polynomial complexity analysis and numerical implementation for a short-step interior point algorithm for monotone linear complementarity problems (LCP) based on karnel function. The analysis is based on a new class of search directions. We establish the global convergence of the algorithm. Furthermore, it is shown that the algorithm has O(n 2.5L), iteration complexity. For its numerical tests some strategies are used and indicate that the algorithm is efficient.