On the Extension of a Mehrotra-Type Algorithm for Semidefinite Optimization
نویسندگان
چکیده
It has been shown in various papers that most interior-point algorithms and their analysis can be generalized to semidefinite optimization. This paper presents an extension of the recent variant of Mehrotra’s predictor-corrector algorithm that was proposed by Salahi et al. (2005) for linear optimization problems. Based on the NT (Nesterov and Todd 1997) direction as Newton search direction it is shown that the iteration-complexity bound of the algorithm is of the same order as that of the corresponding algorithm for linear optimization.
منابع مشابه
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...
متن کاملAn 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...
متن کاملA class of polynomial volumetric barrier decomposition algorithms for stochastic semidefinite programming
Ariyawansa and Zhu [5] have recently proposed a new class of optimization problems termed stochastic semidefinite programs (SSDP’s). SSDP’s may be viewed as an extension of two-stage stochastic (linear) programs with recourse (SLP’s). Zhao [25] has derived a decomposition algorithm for SLP’s based on a logarithmic barrier and proved its polynomial complexity. Mehrotra and Özevin [17] have exten...
متن کاملA Semidefinite Optimization Approach to Quadratic Fractional Optimization with a Strictly Convex Quadratic Constraint
In this paper we consider a fractional optimization problem that minimizes the ratio of two quadratic functions subject to a strictly convex quadratic constraint. First using the extension of Charnes-Cooper transformation, an equivalent homogenized quadratic reformulation of the problem is given. Then we show that under certain assumptions, it can be solved to global optimality using semidefini...
متن کامل