This talk surveys applications of space dilation in the perceptron-like algorithms for solving systems of linear inequalities in polynomial time: from the ellipsoid algorithm to the modified perceptron algorithm and the perceptron rescaling algorithm. It also suggests a more general version of the latter algorithm and poses an open problem about the lowest complexity of this approach. Space dil...

In this paper, we present a new approach for solving absolute value equation (AVE) whichuse Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradientmethods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descentdir...

We present a subgradient extragradient method for solving variational inequalities in Hilbert space. In addition, we propose a modified version of our algorithm that finds a solution of a variational inequality which is also a fixed point of a given nonexpansive mapping. We establish weak convergence theorems for both algorithms.

Polyak's subgradient method for constrained nondifferentiable optimization problems is modified in one respect to improve the computational efficiency. The two consecutive projection operations in Polyak method are combined into a single projection operation. The resulting algorithm has a convergence property which is strictly stronger than that of the original Polyak method. A computational te...

In this paper we develop a new primal-dual subgradient method for nonsmooth convex optimization problems. This scheme is based on a self-concordant barrier for the basic feasible set. It is suitable for finding approximate solutions with certain relative accuracy. We discuss some applications of this technique including fractional covering problem, maximal concurrent flow problem, semidefinite ...

A second-order bundle method to minimize the maximum eigenvalue function François Oustry