In this paper, an interior point algorithm for linear programs is adapted for solving multistage stochastic linear programs. The algorithm is based on Monteiro and Adler’s path-following algorithm for deterministic linear programs. In practice, the complexity of the algorithm is linear with respect to the size of the sample space. The algorithm starts from a feasible solution of the problem and...

We discuss the nonabelian world-volume action which governs the dynamics of N coincident Dp-branes. In this theory, the branes’ transverse displacements are described by matrix-valued scalar fields, and so this is a natural physical framework for the appearance of noncommutative geometry. One example is the dielectric effect by which Dp-branes may be polarized into a noncommutative geometry by ...

Multidisciplinary design optimization (MDO) problems are engineering design problems that require the consideration of the interaction between several design disciplines. Due to certain organizational aspects of MDO problems, decomposition algorithms are often the only feasible solution approach. Two natural decomposition approaches to the MDO problem are bilevel decomposition algorithms and Sc...

This paper establishes the polynomial convergence of a new class of (feasible) primal-dual interior-point path following algorithms for semideenite programming (SDP) whose search directions are obtained by applying Newton method to the symmetric central path equation (P T XP) 1=2 (P ?1 SP ?T)(P T XP) 1=2 ? I = 0; where P is a nonsingular matrix. Speciically, we show that the short-step path fol...

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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.

The rediscovery of the affine scaling method in the late 80s was one of the turning points which led to a new chapter in Modern Optimization the Interior Point Methods (IPMs). The purpose of this paper is to show the intrinsic connections between Interior and Exterior Point methods (EPMs), which have been developed during the last 30 years. A class Ψ of smooth and strictly concave functions ψ :...

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...