Spend your few moment to read a book even only few pages. Reading book is not obligation and force for everybody. When you don't want to read, you can get punishment from the publisher. Read a book becomes a choice of your different characteristics. Many people with reading habit will always be enjoyable to read, or on the contrary. For some reasons, this interior point algorithms theory and an...

In this paper the abstract of the thesis ”New Interior Point Algorithms in Linear Programming” is presented. The purpose of the thesis is to elaborate new interior point algorithms for solving linear optimization problems. The theoretical complexity of the new algorithms are calculated. We also prove that these algorithms are polynomial. The thesis is composed of seven chapters. In the first ch...

A large number of problems in transportation, communications and manufacturing can be modelled as network ow problems. In these problems one seeks to nd the most e cient, or optimal, way to move ow (e.g. materials, information, buses, electrical currents) on a network (e.g. postal network, computer network, transportation grid, power grid). Many of these optimization problems are special classe...

An algorithm for solving linear programming problems can be used as a subroutine in methods for more complicated problems. Such methods usually involve solving a sequence of related linear programming problems, where the solution to one linear program is close to the solution to the next, that is, it provides a warm start for the next linear program. The branch and cut method for solving intege...

Linear Complementarity Problems (LCP s) belong to the class of NP-complete problems. Therefore we can not expect a polynomial time solution method for LCP s without requiring some special property of the matrix coefficient matrix. Our aim is to construct some interior point algorithms which, according to the duality theorem in EP form, gives a solution of the original problem or detects the lac...

We perform a smoothed analysis of the termination phase of an interior-point method. By combining this analysis with the smoothed analysis of Renegar’s interior-point algorithm in [DST02], we show that the smoothed complexity of an interior-point algorithm for linear programming is O(m log(m/σ)). In contrast, the best known bound on the worst-case complexity of linear programming is O(mL), wher...