The modern era of interior-point methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex

to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We also argue that most known interior point methods for linear programs can be transformed in a

We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems, such as max-cut. Other

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The paper describes an interior-point algorithm for nonconvex nonlinear programming which is a direct extension of interior--point methods for linear and quadratic programming. Major modifications include a merit function and an altered search direction to ensure that a descent direction

This article describes the current state of the art of interior-point methods (IPMs) for convex, conic, and general nonlinear optimization. We discuss the theory, outline the algorithms, and comment on the applicability of this class of methods, which have revolutionized the field over the last

in this approach and the proposals that have been made to resolve the difficulties. Then we investigate postoptimal analysis in linear programming from an interior point of view. We make use of the partition of the variables induced by a pair of strictly complementary solutions (the optimal partition), which

The interior point method for linear programming was introduced by Karmakar in 1984. It runs in polynomial time and is a practical method. For many problems it is competitive or superior to the simplex method. Many LP packages, e.g., CPLEX, offer a simplex as well as an interior point method. Links

ABSTRACT. This paper describes a software package, called LOQO, which implements a primaldual interior-point method for general nonlinear programming. We focus in this paper mainly on the algorithm as it applies to linear and quadratic programming with only brief mention of the extensions to convex

These lecture notes aim at developing a thorough understanding of the core theory for interior-point methods. The overall theory continues to grow ata rapid rate but the core ideas have remained largely unchanged for several years, since Nesterov and Nemirovskii [1] published their path