In the contribution, we describe an algorithm for solving nonlinear nonconvex programming problems, which is based on the interior point approach. The main theoretical results concern direction determination and step-length selection. We split inequality constraints into active and inactive parts to overcome problems with instability. Inactive constraints are eliminated directly, while active c...

Interior-point methods feature prominently among numerical methods for inequality-constrained optimization problems, and involve the need to solve a sequence of linear systems that typically become increasingly ill-conditioned with the iterations. To solve these systems, whose original form has a nonsymmetric 3×3 block structure, it is common practice to perform block elimination and either sol...

Linear optimization (LO) is the fundamental problem of mathematical optimization. It admits an enormous number of applications in economics, engineering, science and many other fields. The three most significant classes of algorithms for solving LO problems are: Pivot, Ellipsoid and Interior Point Methods. Because Ellipsoid Methods are not efficient in practice we will concentrate on the comput...

Support vector machine training can be represented as a large quadratic program. We present an efficient and numerically stable algorithm for this problem using primaldual interior point methods. Reformulating the problem to exploit separability of the Hessian eliminates the main source of computational complexity, resulting in an algorithm which requires only O(n) operations per iteration. Ext...

Phenotype phase plane analysis is a linear optimization procedure which can be used to study the value of the objective function (a desired phenotype) as two variables (external substrates) vary simultaneously. Existing methods for phenotype phase plane analysis are based on computing shadow prices as defined in classical linear programming duality theory. Since different bases may produce diff...

Some implementations of interior-point algorithms obtain their search directions by solving symmetric indeenite systems of linear equations. The conditioning of the coeecient matrices in these so-called augmentedsystems deteriorateson later iterations, as some of the diagonal elements grow without bound. Despite this apparent diiculty, the steps produced by standard factorization procedures are...

In this paper we treat numerical computation methods for linear programming. Started from the analysis of the efficiency and defficiency of the simplex procedure, we present new possibilities offered by the interior-point methods, which appears from practical necessity, from the need of efficient means of solving large-scale problems. We realise the implementation in Java of the Karmarkar’s met...

Abstract. In this paper a duality of transformation functions in the interior point method is treated. A dual pair of convex or linear programming problems is considered and the primal problem is transformed by the parametrized transformation function of a more general form than logarithmic is. The construction of the parametrized transformation function for the dual problem is carried out so t...

This research studies two computational techniques that improve the practical performance of existing implementations of interior point methods for linear programming. Both are based on the concept of symmetric neighbourhood as the driving tool for the analysis of the good performance of some practical algorithms. The symmetric neighbourhood adds explicit upper bounds on the complementarity pai...

No part of this Journal may be reproduced in any form, by print, photoprint, mi-croolm or any other means without written permission from Faculty of Technical The publication of Karmarkar's paper has resulted in intense research activity into interior{point algorithms for linear programming. Degeneracy is present in most real{life problems and has always been an important issue in linear progra...