Proximal ACCPM is a variant of the analytic center cutting plane method, in which a proximal term is added to the barrier function that defines the center. The present paper gives a detailed presentation of the method and of its implementation. Proximal ACCPM is used to solve the Lagrangian relaxation of the p-median problem on two sets of problem instances. Problems of the same collection are ...

The educational testing problem is a convex non-smooth optimization problem. We recast the problem so that classical non-smooth optimization techniques such as the ellipsoid method can be readily applicable. Attention is paid to Dikin's method where a special barrier function and interior ellipsoids for the feasible domain are explicitly formulated. The implementation is much easier than that b...

In this paper we present a generic primal-dual interior point methods (IPMs) for linear optimization in which the search direction depends on a univariate kernel function which is also used as proximity measure in the analysis of the algorithm. The proposed kernel function does not satisfy all the conditions proposed in [2]. We show that the corresponding large-update algorithm improves the ite...

The objective of this study was to evaluate the reduction in skin barrier function caused by direct current iontophoresis by measuring resistance in the short term. The experiments were carried out using rat abdominal skin in vivo. The resistance was measured every 125 ms and analyzed using a two-compartment model consisting of surface and skin resistance. Moreover, the initial value and the ra...

Based on previous theoretical results we present in this paper a global estimation scheme for solving the stable 2D autoregressive filter problem. The different algorithms are based on the traditional Newton method and on the log barrier method that is employed in semi-definite programming. The Newton method is the faster one but the barrier method ensures that the iterates stay in the cone of ...

We present an interior-point penalty method for nonlinear programming (NLP), where the merit function consists of a piecewise linear penalty function (PLPF) and an `2-penalty function. The PLPF is defined by a set of penalty parameters that correspond to break points of the PLPF and are updated at every iteration. The `2-penalty function, like traditional penalty functions for NLP, is defined b...

This paper considers strategies for selecting the barrier parameter at every iteration of an interior-point method for nonlinear programming. Numerical experiments suggest that adaptive choices, such as Mehrotra’s probing procedure, outperform static strategies that hold the barrier parameter fixed until a barrier optimality test is satisfied. A new adaptive strategy is proposed based on the mi...

the aim of this study was to investigate the barrier properties of cellulose nanocrystals-pvananocomposites. nanocomposite films with different filler loading levels (3, 6, 9 and 12% by wt) weredeveloped by solvent casting method. the effect of cellulose nanocrystals on the barrier properties ofthe nanocomposites was studied. to this end, moisture absorption, water vapor permeability (wvp),oxyg...

Hyperbolic polynomials have their origins in partial diierential equations. We show in this paper that they have applications in interior point methods for convex programming. Each homogeneous hyperbolic polynomial p has an associated open and convex cone called its hyperbolicity cone. We give an explicit representation of this cone in terms of polynomial inequalities. The function F (x) = ? lo...