A generic primal-dual interior-point method for semidefinite optimization based on a new class of kernel functions

An Interior Point Algorithm for Solving Convex Quadratic Semidefinite Optimization Problems Using a New Kernel Function

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...

A path following interior-point algorithm for semidefinite optimization problem based on new kernel function

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 sho...

New complexity analysis of a full Nesterov-Todd steps IIPM for semidefinite optimization

An interior-point algorithm for $P_{ast}(kappa)$-linear complementarity problem based on a new trigonometric kernel function

In this paper, an interior-point algorithm  for $P_{ast}(kappa)$-Linear Complementarity Problem (LCP) based on a new parametric trigonometric kernel function is proposed. By applying strictly feasible starting point condition and using some simple analysis tools, we prove that our algorithm has $O((1+2kappa)sqrt{n} log nlogfrac{n}{epsilon})$ iteration bound for large-update methods, which coinc...

ISSN 0333-3590 Primal-Dual IPMS for Semidefinite Optimization Based on Finite Barrier Functions

In this paper we extend the results obtained for a class of finite kernel functions by Y.Q. Bai M. El Ghami and C.Roos published in SIAM Journal of Optimization, 13(3):766–782, 2003 [3] for linear optimization to semidefinite optimization. We show that the iteration bound for primal dual methods is O( √ n log n log n ), for large-update methods andO( √ n log n ), for small-update methods. The i...