A practical warm-start procedure is described for the infeasible primal-dual interior-point method employed to solve the restricted master problem within the cutting-plane method. In contrast to the theoretical developments in this eld, the approach presented in this paper does not make the unrealistic assumption that the new cuts are shallow. Moreover, it treats systematically the case when a ...

Primal-dual Interior-Point Methods (IPMs) have shown their ability in solving large classes of optimization problems efficiently. Feasible IPMs require a strictly feasible starting point to generate the iterates that converge to an optimal solution. The self-dual embedding model provides an elegant solution to this problem with the cost of slightly increasing the size of the problem. On the oth...

Re-optimization techniques for an interior point method applied to solve a sequence of linear programming problems are discussed. Conditions are given for problem perturbations that can be absorbed in merely one Newton step. The analysis is performed for both short-step and long-step feasible path-following method. A practical procedure is then derived for an infeasible path-following method. I...

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...

The knowledge of the interior structure of buildings is important in many civilian and military applications. While it is possible to obtain interior maps by exhaustively inspecting every room in a building, in many situations this is infeasible due to security or safety reasons. In this paper, we develop a method to generate interior building floor plans from the exterior of the structure. We ...

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...

In many infeasible linear programs it is important to construct it to a feasible problem with a minimum pa-rameters changing corresponding to a given nonnegative vector. This paper defines a new inverse problem, called “inverse feasible problem”. For a given infeasible polyhedron and an n-vector a minimum perturba-tion on the parameters can be applied and then a feasible polyhedron is concluded.

This paper discusses computational experiments with linear optimization problems involving semidefinite, quadratic, and linear cone constraints (SQLPs). Many test problems of this type are solved using a new release of SDPT3, a Matlab implementation of infeasible primal-dual path-following algorithms. The software developed by the authors uses Mehrotratype predictor-corrector variants of interi...

Infeasible-Interior-Point methods shown in previous homeworks are well behaved when the number of constraints are small and the dimension of the energy function domain is also small. This fact is easily seen, since each iteration of such methods requires of solving a linear equation system whose size depends precisely on the number of constraints and the dimension of the search space. In additi...

We propose a polynomial algorithm for linear programming. The algorithm represents a linear optimization or decision problem in the form of a system of linear equations and non-negativity constraints. Then it uses a procedure that either finds a solution for the respective homogeneous system or provides the information based on which the algorithm rescales the homogeneous system so that its fea...