Asymptotic Behavior of HKM Paths in Interior Point Method for Monotone Semidefinite Linear Complementarity Problem: General Theory

Abstract An interior point method (IPM) defines a search direction at an interior point of the feasible region. These search directions form a direction field which in turn defines a system of ordinary differential equations (ODEs). Thus, it is natural to define the underlying paths of the IPM as the solutions of the systems of ODEs. In Then we show that if the given SDLCP has a unique solution, the first derivative of its off-central path, as a function of √ µ, is bounded. We work under the assumption that the given SDLCP satisfies strict complementarity condition

Log-barrier decomposition methods for solving stochastic programs

An algorithm incorporating the logarithmic barrier into the decomposition technique is proposed for solving stochastic programs. Basic properties concerning the existence and uniqueness of the solution and the underlying path are studied. The algorithm is shown to converge globally at the linear rate and to run in polynomial-time

Interior Point Methods with Decomposition for Linear Programs

This paper deals with an algorithm which incorporates the interior point method into the Dantzig-Wolfe decomposition technique for solving large-scale linear programming problems. At each iteration, the algorithm performs one step of Newton's method to solve a subproblem, obtaining an approximate solution, which is then used to compute an approximate Newton direction to find a new vector of the Lagrange multipliers. We show that the algorithm is globally linearly convergent and has the polynomial-time complexity. Key Words: Large-scale linear programming, Interior point methods, Dantzig-Wolfe decomposition, Complexity. Abbreviated Title: Interior point methods with decomposition AMS(MOS) subject classifications: 90C05, 90C06, 90C60. 1. Introduction This paper presents and analyzes an algorithm which incorporates the interior point method into the Dantzig-Wolfe decomposition method. Our concern in this paper is to show the polynomial-time complexity of the algorithm. In order to explo..