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 show that the worst-case iteration bound for our IPM is O(۶(m+۱)^{\frac{۳m+۴}{۲(m+۱)}}\Psi _{۰}^{\frac{m+۲}{۲(m+۱)}}\frac{۱}{\theta }\log \frac{n\mu ^{۰}}{\varepsilon }), where m>۴.

کلیدواژه ها:

quadratic programming ، convex nonlinear programming ، interior point methods