In this paper, we propose a large-update interior-point algorithm for linear optimization based on a new kernel function. New search directions and proximity measure are defined based on this kernel function. We show that if a strictly feasible starting point is available, then the new algorithm has log iteration complexity.

In this paper we clarify that the interior proximal method developed in [6] (vol. 27 of this journal) for solving variational inequalities with monotone operators converges under essentially weaker conditions concerning the functions describing the ”feasible” set as well as the operator of the variational inequality.

Using a simple analytical example, we demonstrate that a class of interior point methods for general nonlinear programming, including some current methods, is not globally convergent. It is shown that those algorithms do produce limit points that are neither feasible nor stationary points of some measure of the constraint violation, when applied to a well-posed problem.

We present ellipsoid algorithms for convexly constrained estimation and design problems. The proposed polynomial time algorithms yield both an estimate of the complete set of feasible solutions and a point estimate in the interior. Optimal cutting hyperplanes are derived, and a computation-ally eecient sequential cut algorithm is proven to provide estimation performance achieving the best exist...

In this paper, we introduce an aane scaling algorithm for semideenite programming, and give an example of a semideenite program such that the aane scaling algorithm converges to a non-optimal point. Both our program and its dual have interior feasible solutions, and unique optimal solutions which satisfy strict complementarity, and they are nondegenerate everywhere. Abbreviated Title: AAne scal...

Given a nite number of closed convex sets whose algebraic representation is known, we study the problem of optimizing a convex function over the closure of the convex hull of the union of these sets. We derive an algebraic characterization of the feasible region in a higher-dimensional space and propose a solution procedure akin to the interior-point approach for convex programming.

In this paper, we present an implementing weighted path following interior point algorithm for solving linear complementarity problems. Different strategies are used for its numerical implementation. An artificial variable technique is used to compute a strictly feasible starting point. An interesting comparison with the well-known Lemke’s algorithm is done.

We apply the dressing method to a string solution given by a static string wrapped around the equator of a three-sphere and find that the result is the single spike solution recently discussed in the literature. Further application of the method allows the construction of solutions with multiple spikes. In particular we construct the solution describing the scattering of two single spikes and c...

In this article, a procedure for characterizing the feasible parameter set of nonlinear models with a membershipset uncertainty description is provided. A specific Genetic Algorithm denominated ε-GA has been developed, based on Evolutionary Algorithm for Multiobjective Optimization, to find the global minima of the multimodal functions appeared when the robust identification problem is formulat...

We propose a polynomial algorithm for linear programming. The algorithm represents a linear optimization or decision problem in the form of a system of linear equations and non-negativity constraints. Then it uses a procedure that either finds a solution for the respective homogeneous system or provides the information based on which the algorithm rescales the homogeneous system so that its fea...