The corner relaxation of a mixed-integer linear program is a central concept in cutting plane theory. In a recent paper Fischetti and Monaci provide an empirical assessment of the strength of the corner and other related relaxations on benchmark problems. In this paper we give a precise characterization of the bounds given by these relaxations … Read more
We relate a deterministic Kalman filter on semi-infinite interval to linear-quadratic tracking control model with unfixed initial condition CitationTechnical report, University of Notre Dame, October, 2011ArticleDownload View PDF
We propose a framework of lower bounds for the asymmetric traveling salesman problem (TSP) based on approximating the dynamic programming formulation with diff erent basis vector sets. We discuss how several well-known TSP lower bounds correspond to intuitive basis vector choices and give an economic interpretation wherein the salesman must pay tolls as he travels between … Read more
Considering the minmax programming problem, lower and upper subdi erential optimality conditions, in the sense of Mordukhovich, are derived. The approach here, mainly based on the nonsmooth dual objects of Mordukhovich, is completely di erent from that of most of the previous works where generalizations of the alternative theorem of Farkas have been applied. The results obtained … Read more
We consider the economic lot-sizing game with general concave ordering cost functions. It is well-known that the core of this game is nonempty when the inventory holding costs are linear. The main contribution of this work is a combinatorial, primal-dual algorithm that computes a cost allocation in the core of these games in polynomial time. … Read more
The crossing number of a graph is the minimal number of edge crossings achievable in a drawing of the graph in the plane. The crossing numbers of complete and complete bipartite graphs are long standing open questions. In a 2-page drawing of a graph, all vertices are drawn on a circle, and no edge may … Read more
We propose a method to solve nonlinear second-order cone programs (SOCPs), based on a continuously differentiable exact penalty function. The construction of the penalty function is given by incorporating a multipliers estimate in the augmented Lagrangian for SOCPs. Under the nondegeneracy assumption and the strong second-order sufficient condition, we show that a generalized Newton method … Read more
We study the problem of constructing confidence intervals for the optimal value of a stochastic programming problem by using bootstrapping. Bootstrapping is a resampling method used in the statistical inference of unknown parameters for which only a small number of samples can be obtained. One such parameter is the optimal value of a stochastic optimization … Read more
We give explicit formulas for the subdifferential set of the conjugate of non necessarily convex functions defined on general Banach spaces. Even if such a subdifferential mapping takes its values in the bidual space, we show that up to a weak** closure operation it is still described by using only elements of the initial space … Read more
We compare two recent variational-analytic approaches to second-order conditions and sensitivity analysis for nonsmooth optimization. We describe a broad setting where computing the generalized Hessian of Mordukhovich is easy. In this setting, the idea of tilt stability introduced by Poliquin and Rockafellar is equivalent to a classical smooth second-order condition. ArticleDownload View PDF