Asymptotic Behavior of Interior-Point Methods: A View From Semi-Infinite Programming

Interior-point algorithms for semi-infinite programming

An interior point algorithm for semi-infinite linear programming

We consider the generalization of a variant of Karmarkar's algorithm to semi-infinite programming. The extension of interior point methods to infinite-dimensional linear programming is discussed and an algorithm is derived. An implementation of the algorithm for a class of semi-infinite linear programs is described and the results of a number of test problems are given. We pay particular attent...

A Computational View of Interior Point Methods

Many issues that are crucial for an e cient implementation of an interior point algorithm are addressed in this chapter. To start with, a prototype primaldual algorithm is presented. Next, many tricks that make it e cient in practice are discussed in detail. Those include: preprocessing techniques, initialization approaches, methods for computing search directions (and the underlying linear alg...

Proximal Interior Point Approach for Solving Convex Semi-infinite Programming Problems

1 A regularized logarithmic barrier method for solving ill-posed convex semi-infinite programming problems is considered. In this method a multistep proximal regularization is coupled with an adaptive discretization strategy in the framework of the interior point approach. Termination of the proximal iterations at each discretization level is controlled by means of estimates, characterizing the...

Interior Point Methods and Linear Programming

The linear programming problem is usually solved through the use of one of two algorithms: either simplex, or an algorithm in the family of interior point methods. In this article two representative members of the family of interior point methods are introduced and studied. We discuss the design of these interior point methods on a high level, and compare them to both the simplex algorithm and ...