We present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a self-contained convergence analysis, that uses the formalism of the theory of self-concordant fucntions, but for the main results, we give...

This paper adopts a normative approach to catastrophe insurance. It addresses the question of how innovations in the design of insurance contracts could help resolve the capacity gap in the provision of insurance against natural catastrophes. It extends previous research with the same approach...

This paper presents a new primal-dual algorithm for solving a class of monotropic programming problems. This class involves many problems arising in a number of important applications in telecommunications networks, transportation and water distribution. The proposed algorithm is inspired by...

In this paper we study special barrier functions for the convex cones, which are the sum of a self-concordant barrier for the cone and a positive-semidefinite quadratric form. We show that the central path of these augmented barrier functions can be traced with linear speed. We also study the...

We describe the analytic center cutting plane method and its relationship to classical methods of nondifferentiable optimization and column generation. Implementations issues are also discussed, and current applications listed.

A new concept is proposed for linking algebraic modeling languages and the structure exploiting solver.

Stochastic programs inevitably get huge if they are to model real life problems accurately. Nowadays only massive parallel machines can solve them but at a cost few decision makers can afford. We report hereon a deterministic equivalent linear programming model of 1,111,112 constraints and...

This paper presents linear algebra techniques used in the implementation of an interior point method for solving linear programs and convex quadratic programs with linear constraint. The new regularization techniques for Newton equation system applicable to both symmetric positive definite and...