Interior point methods for optimization have been around for more than 25 years now. Their presence has shaken up the field of optimization. Interior point methods for linear and (convex) quadratic programming display several features which make them particularly attractive for very large scale optimization. Among the most impressive of them are their lowdegree polynomial worst-case complexity ...

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...

In this paper we use interior-point methods for linear programming, developed in t,he contest of sequential computation, to obtain a parallel algorithm for t,he bipartite matching problem. Our algorithm runs in 0*(,/E) time I. Our results extend to the weighted bipartite matching problem and to the zero-one minimum-cost flow problem, yielding O*( filog C’) algorithms?. This improvk’previous bou...

In this paper we study interior point trajectories in semideenite programming (SDP) including the central path of an SDP. This work was inspired by the seminal work by Megiddo on linear programming trajectories 15]. Under an assumption of primal and dual strict feasibility , we show that the primal and dual central paths exist and converge to the analytic centers of the optimal faces of, respec...

PROOF. Let U be an open neighborhood of x. By Lemma 4 there exists a compact set M in T such that xMC U and HQSM*. Let V be a neighborhood of x for which VMQ U. There exists an admissible set A such that AC.2 and xAQV. Hence xAMCU. Define B = SfY4 ikf. Since A QBM", B is an admissible set. Also BC.S and xBQU. The proof is completed. The following theorem is an immediate consequence of Lemmas 5 ...

Interior Point Stabilization (IPS) is an acceleration method for Column Generation algorithms. Like previous stabilization techniques, it addresses degeneracy problems and convergence difficulties by preventing dual variables from taking extreme values. IPS is however different since it selects a dual solution inside the optimal dual space rather than retrieving an extreme point solution from t...

Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivalent nonconvex quadratic programming problem, interior point methods for solving network flow probl...

Spatial reserve design concerns the planning of biological reserves for conservation. Typical reserve selection formulations operate on a large set of landscape elements, which could be grid cells or irregular sites, and selection algorithms aim to select the set of sites that achieves biodiversity target levels with minimum cost. This study presents a completely different optimization approach...

Polynomial cutting plane methods based on the logarithmic barrier function and on the volumetric center are surveyed. These algorithms construct a linear programming relaxation of the feasible region, find an appropriate approximate center of the region, and call a separation oracle at this approximate center to determine whether additional constraints should be added to the relaxation. Typical...