We consider a homogeneous self-dual interior point algorithm for solving multistage stochastic linear programs. The algorithm is particularly suitable for the so-called “scenario formulation” of the problem, whose constraint system consists of a large block-diagonal matrix together with a set of sparse nonanticipativity constraints. Due to this structure, the major computational work required b...

In this paper, we show that the moving directions of the primal-affine scaling method (with logarithmic barrier function), the dual-affine scaling method (with logarithmic barrier function), and the primal-dual interior point method are merely the Newton directions along three different algebraic "paths" that lead to a solution of the Karush-Kuhn-Tucker conditions of a given linear programming ...

We present the convergence analysis of the inexact infeasible pathfollowing (IIPF) interior-point algorithm. In this algorithm, the preconditioned conjugate gradient method is used to solve the reduced KKT system (the augmented system). The augmented system is preconditioned by using a block triangular matrix. The KKT system is solved approximately. Therefore, it becomes necessary to study the ...

In the context of helical cone-beam CT, Danielsson et al. discovered that for each point interior to the cylindrical surface containing a given helix, there is exactly one line segment passing through the point which intersects two points less than one turn apart on the helix. This segment is called a π-line. A new constructive algebraic proof of this result is presented along with a fast algor...

In this paper, we outline a bilevel approach for solving mixed integer nonlinear programming problems. The approach combines a branch-and-bound algorithm in the outer iterations and an infeasible interior-point method in the inner iterations. We report on the details of the implementation, including the efficient pruning of the branch-and-bound tree via equilibrium constraints, warmstart strate...

Discrete optimal transport problems give rise to very large linear programs (LPs) with a particular structure of the constraint matrix. In this paper, we present hybrid algorithm that mixes an interior point method (IPM) and column generation, specialized for LP originating from Kantorovich problem. Knowing solutions such display high degree sparsity, propose generation–like technique force all...

Abstract In this paper, we propose a new long-step interior point method for solving sufficient linear complementarity problems. The algorithm combines two important approaches from the literature: main ideas of introduced by Ai and Zhang algebraic equivalent transformation technique proposed Darvay. Similar to Zhang, our also works in wide neighborhood central path has best known iteration com...