We present an algorithm for the constrained saddle point problem with a convexconcave function L and convex sets with nonempty interior. The method consists of moving away from the current iterate by choosing certain perturbed vectors. The values of gradients of L at these vectors provide an appropriate direction. Bregman functions allow us to define a curve which starts at the current iterate ...

in this paper, we describe our implementation of an interior point algorithm for large scale systems. first we identify system with small and medium methods convex optimization, then we use interior point method for identification. finally we offer an interior point method that uses nonlinear cost function and see that we achieve a good trade-off between error and cpu time. actually, in this pa...

In each iteration of an interior-point method for semideenite programming, the maximum step-length that can be taken by the iterate while maintaining the positive semideeniteness constraint need to be estimated. In this note, we show how the maximum step-length can be estimated via the Lanczos iteration, a standard iterative method for estimating the extremal eigenvalues of a matrix. We also gi...

We consider the problem of !nding a linear iteration that yields distributed averaging consensus over a network, i.e., that asymptotically computes the average of some initial values given at the nodes. When the iteration is assumed symmetric, the problem of !nding the fastest converging linear iteration can be cast as a semide!nite program, and therefore e"ciently and globally solved. These op...

A linear program has a unique least 2-norm solution provided that the linear program has a solution. To locate this solution, most of the existing methods were devised to solve certain equivalent perturbed quadratic programs or unconstrained minimization problems. Different from these traditional methods, we provide in this paper a new theory and an effective numerical method to seek the least ...