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
In this article we establish for the first time the well-posedness of the shooting algorithm applied to optimal control problems for which all control variables enter linearly in the Hamil- tonian. We start by investigating the case having only initial-final state constraints and free control variable, and afterwards we deal with control bounds. The shooting … Read more
This paper deals with optimal control problems for systems that are affine in one part of the control variables and nonlinear in the rest of the control variables. We have finitely many equality and inequality constraints on the initial and final states. First we obtain second order necessary and sufficient conditions for weak optimality. Afterwards, … 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
In this paper, we propose a new robust cycle-based control policy for single installation inventory models with non-stationary uncertain demand. The policy is simple, flexible, easily implementable and preliminary numerical experiments suggest that the policy has very promising empirical performance. The policy can be used both when the excess demand is backlogged as well as … Read more