Steplengths in interior-point algorithms of quadratic programming

Steplengths in interior-point algorithms of quadratic programming

An approach to determine primal and dual stepsizes in the infeasible{ interior{point primal{dual method for convex quadratic problems is presented. The approach reduces the primal and dual infeasibilities in each step and allows diierent stepsizes. The method is derived by investigating the eecient set of a multiobjective optimization problem. Computational results are also given.

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...

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...

Interior-point algorithms for semi-infinite programming

Steplength selection in interior-point methods for quadratic programming

We present a new strategy for choosing primal and dual steplengths in a primal-dual interior-point algorithm for convex quadratic programming. Current implementations often scale steps equally to avoid increases in dual infeasibility between iterations. We propose that this method can be too conservative, while safeguarding an unequally-scaled steplength approach will often require fewer steps ...