Interior-point algorithms for 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...

Interior Point Algorithms for Integer Programming

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...

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...

New Interior Point Algorithms in Linear Programming †

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...