Solving Real World Linear Ordering Problems Using a Primal Dual Interior Point Cutting Plane Method
نویسندگان
چکیده
Cutting plane methods require the solution of a sequence of linear programs where the solution to one provides a warm start to the next A cutting plane algorithm for solving the linear ordering problem is described This algorithm uses the primal dual interior point method to solve the linear programming relaxations A point which is a good warm start for a simplex based cutting plane algorithm is generally not a good starting point for an interior point method Techniques used to improve the warm start include attempting to identify cutting planes early and storing an old feasible point which is used to help recenter when cutting planes are added Computational results are de scribed for some real world problems the algorithm appears to be competitive with a simplex based cutting plane algorithm Research partially supported by ONR Grant number N J
منابع مشابه
1 Solving Linear Ordering Problems with a Combined Interior Point / Simplex Cutting Plane Algorithm
We describe a cutting plane algorithm for solving linear ordering problems. The algorithm uses a primal-dual interior point method to solve the rst few relaxations and then switches to a simplex method to solve the last few relaxations. The simplex method uses CPLEX 4.0. We compare the algorithm with one that uses only an interior point method and with one that uses only a simplex method. We so...
متن کاملInterior Point and Semidefinite Approaches in Combinatorial Optimization
Conic programming, especially semidefinite programming (SDP), has been regarded as linear programming for the 21st century. This tremendous excitement was spurred in part by a variety of applications of SDP in integer programming (IP) and combinatorial optimization, and the development of efficient primal-dual interior-point methods (IPMs) and various first order approaches for the solution of ...
متن کاملAn Interior Point Algorithm for Solving Convex Quadratic Semidefinite Optimization Problems Using a New Kernel Function
In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...
متن کاملWarm Start and "-subgradients in Cutting Plane Scheme for Block-angular Linear Programs
This paper addresses the issues involved with an interior point-based decomposition applied to the solution of linear programs with a block-angular structure. Unlike classical decomposition schemes that use the simplex method to solve subproblems, the approach presented in this paper employs a primal-dual infeasible interior point method. The above-mentioned algorithm ooers a perfect measure of...
متن کاملWarm Start and ε-Subgradients in a Cutting Plane Scheme for Block-Angular Linear Programs
This paper addresses the issues involved with an interior point-based decomposition applied to the solution of linear programs with a block-angular structure. Unlike classical decomposition schemes that use the simplex method to solve subproblems, the approach presented in this paper employs a primal-dual infeasible interior point method. The abovementioned algorithm o ers perfect measure of th...
متن کامل