Robust state estimation using mixed integer programming

This letter describes a robust state estimator based on the solution of a mixed integer program. A tolerance range is associated with each measurement and an estimate is chosen to maximize the number of estimated measurements that remain within tolerance (or equivalently minimize the number of measurements out of tolerance). Some small-scale examples are given which suggest that this approach is robust in the presence of gross errors, is not susceptible to leverage points, and can solve some pathological cases that have previously caused problems for robust estimation algorithms

Portfolio construction through mixed integer programming

Title from cover. "May, 1998."Includes bibliographical references (p. 20).Dimitris Bertsimas, Christopher Darnell and Robert Soucy

On convergence in mixed integer programming

Let $${P \subseteq {\mathbb R}^{m+n}}$$ be a rational polyhedron, and let P I be the convex hull of $${P \cap ({\mathbb Z}^m \times {\mathbb R}^n)}$$ . We define the integral lattice-free closure of P as the set obtained from P by adding all inequalities obtained from disjunctions associated with integral lattice-free polyhedra in $${{\mathbb R}^m}$$ . We show that the integral lattice-free closure of P is again a polyhedron, and that repeatedly taking the integral lattice-free closure of P gives P I after a finite number of iterations. Such results can be seen as a mixed integer analogue of theorems by Chvátal and Schrijver for the pure integer case. One ingredient of our proof is an extension of a result by Owen and Mehrotra. In fact, we prove that for each rational polyhedron P, the split closures of P yield in the limit the set P

Revisiting lagrange relaxation (LR) for processing large-scale mixed integer programming (MIP) problems

Lagrangean Relaxation has been successfully applied to process many well known instances of NP-hard Mixed Integer Programming problems. In this paper we present a Lagrangean Relaxation based generic solver for processing Mixed Integer Programming problems. We choose the constraints, which are relaxed using a constraint classification scheme. The tactical issue of updating the Lagrange multiplier is addressed through sub-gradient optimisation; alternative rules for updating their values are investigated. The Lagrangean relaxation provides a lower bound to the original problem and the upper bound is calculated using a heuristic technique. The bounds obtained by the Lagrangean Relaxation based generic solver were used to warm-start the Branch and Bound algorithm; the performance of the generic solver and the effect of the alternative control settings are reported for a wide class of benchmark models. Finally, we present an alternative technique to calculate the upper bound, using a genetic algorithm that benefits from the mathematical structure of the constraints. The performance of the genetic algorithm is also presented

Degrees of cooperation in household consumption models: a revealed preference analysis

We develop a revealed preference approach to analyze non-unitary consumption models with intrahousehold allocations deviating from the cooperative (or Pareto efficient) solution. At a theoretical level, we establish revealed preference conditions of household consumption models with varying degrees of cooperation. Using these conditions, we show independence (or non-nestedness) of the different (cooperative-noncooperative) models. At a practical level, we show that our characterization implies testable conditions for a whole spectrum of cooperative-noncooperative models that can be verified by means of mixed integer programming (MIP) methods. This MIP formulation is particularly attractive in view of empirical analysis. An application to data drawn from the Russia Longitudinal Monitoring Survey (RLMS) demonstrates the empirical relevance of consumption models that account for limited intrahousehold cooperation.household consumption, intrahousehold cooperation, revealed preferences, Generalized Axiom of Revealed Preference (GARP), mixed integer programming (MIP).