Portfolio optimization problems involving Value-at-Risk (VaR) are often computationally intractable and require complete information about the return distribution of the portfolio constituents, which is rarely available in practice. These difficulties are compounded when the portfolio contains derivatives. We develop two tractable conservative approximations for the VaR of a derivative portfolio by evaluating the worst-case VaR … Read more
The Sherali-Adams lift-and-project hierarchy is a fundamental construct in integer programming, which provides successively tighter linear programming relaxations of the integer hull of a polytope. We initiate a new approach to understanding the Sherali-Adams procedure by relating it to methods from computational algebraic geometry. Our main result is a refinement of the Sherali-Adams procedure that … Read more
In this paper, we are concerned with the stability of the error bounds for semi-infinite convex constraint systems. Roughly speaking, the error bound of a system of inequalities is said to be stable if all its “small” perturbations admit a (local or global) error bound. We first establish subdifferential characterizations of the stability of error … Read more
Arc-search is developed in optimization algorithms. In this paper, simple analytic arcs are used to approximate the central path of the linear programming. The primal-dual path-following interior-point method is then used to search optimizers along the arcs for linear programming. They require fewer iterations to find the optimal solutions in all the tested problems in … Read more
Automatic verification of computer code is of paramount importance in embedded systems supplying essential services. One of the most important verification techniques is static code analysis by abstract interpretation: the concrete semantics of a programming language (i.e.the values $\chi$ that variable symbols {\tt x} appearing in a program can take during its execution) are replaced … Read more
The approach of estimate sequence offers an interesting rereading of a number of accelerating schemes proposed by Nesterov. It seems to us that this framework is the most appropriate descriptive framework to develop an analysis of the sensitivity of the schemes to approximations. We develop in this work a simple, self-contained, and unified framework for … Read more
In an important paper, Burer recently showed how to reformulate general mixed-binary quadratic optimization problems (QPs) into copositive programs where a linear functional is minimized over a linearly constrained subset of the cone of completely positive matrices. In this note we interpret the implication from a topological point of view, showing that the Minkowski sum … Read more
We present an alternating direction method based on an augmented Lagrangian framework for solving semidefinite programming (SDP) problems in standard form. At each iteration, the algorithm, also known as a two-splitting scheme, minimizes the dual augmented Lagrangian function sequentially with respect to the Lagrange multipliers corresponding to the linear constraints, then the dual slack variables … Read more
We consider a generalization of the well known greedy algorithm, called $m$-step greedy algorithm, where $m$ elements are examined in each iteration. When $m=1$ or $2$, the algorithm reduces to the standard greedy algorithm. For $m=3$ we provide a complete characterization of the independence system, called trioid, where the $m$-step greedy algorithm guarantees an optimal … Read more
This paper proposes a linear integer programming formulation and several heuristics based on GRASP and path relinking for the antibandwidth problem. In the antibandwidth problem, one is given an undirected graph with N nodes and must label the nodes in a way that each node receives a unique label from the set {1, 2, …, … Read more