Since the financial crisis in 2007-2008, the vulnerability of a financial system has become a major concern in financial engineering. In this paper, we analyze the vulnerability of a financial network based on the linear optimization model introduced by Eisenberg and Noe (2001), where the right...

In this paper, we consider an optimal portfolio de-leveraging problem, where the objective is to meet specified debt/equity requirements at the minimal execution cost. Permanent and temporary price impact is taken into account. With no restrictions on the relative magnitudes of permanent and...

This brief note presents a personal recollection of the early history of EUROpt, the Continuous Optimization Working Group of EURO. This historical note details the events that happened before the formation of EUROpt Working Group and the first five years of its existence. During the early years...

In this chapter we describe the optimal set approach for sensitivity analysis for LP. We show that optimal partitions and optimal sets remain constant between two consecutive transition-points of the optimal value function. The advantage of using this approach instead of the classical approach...

In this chapter we describe the optimal set approach for sensitivity analysis for LP. We show that optimal partitions and optimal sets remain constant between two consecutive transition-points of the optimal value function. The advantage of using this approach instead of the classical approach...

In this paper we deal with sensitivity analysis in convex quadratic programming, without making assumptions on nondegeneracy, strict convexity of the objective function, and the existence of a strictly complementary solution. We show that the optimal value as a function of a right--hand side...

Optimal solutions of interior point algorithms for linear and quadratic programming and linear complementarity problems provide maximal complementary solutions. Maximal complementary solutions can be characterized by optimal (tri)partitions. On the other hand, the solutions provided by...