We propose a new class of primal-dual methods for linear optimization (LO). By using some new analysis tools, we prove that the large update method for LO based on the new search direction has a polynomial complexity $O\br{n^{\frac{4}{4+\rho}}\log\frac{n}{\e}}$ iterations where $\rho\in [0,2]$ is a parameter used in the system defining the search direction. If $\rho=0$, our results reproduce the well known complexity of the standard primal dual Newton method for LO. At each iteration, our algorithm needs only to solve a linear equation system. An extension of the algorithms to semidefinite optimization is also presented.

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View A New Class of Polynomial Primal-Dual Methods for Linear and Semidefinite Optimization