This paper is devoted to optimality conditions for nonsmooth quasiconcave programming. Arrow and Enthoven (1961) formulate several economic problems into quasiconcave programming, and give a sufficient condition for smooth quasiconcave programming in their epoch-making and comprehensive paper. In this paper, generalized necessary and sufficient conditions for nonsmooth quasiconcave programming have been derived in terms of … Read more
A convex variational framework is proposed for solving inverse problems in Hilbert spaces with a priori information on the representation of the target solution in a frame. The objective function to be minimized consists of a separable term penalizing each frame coefficient individually and of a smooth term modeling the data formation model as well … Read more
This paper proposes a control parametrization under Model Predictive Controller (MPC) framework for constrained linear discrete time systems with bounded additive disturbances. The proposed approach has the same feasible domain as that obtained from parametrization over the family of time-varying state feedback policies. In addition, the closed-loop system is stable in the sense that the … Read more
Hayrapetyan, Tardos and Wexler recently introduced a framework to study the impact of collusion in congestion games on the quality of Nash equilibria. We adopt their framework to network games and focus on the well established price of anarchy as a measure of this impact. We first investigate nonatomic network games with coalitions. For this … Read more
We construct an integrated multi-period inventory-production-distribution replenishment plan for three-stage supply chains. The supply chain maintains close-relationships with a small group of suppliers, and the nature of the products (bulk, chemical, etc.) makes it more economical to rely upon a direct shipment, full-truck load distribution policy between supply chain nodes. In this paper, we formulate … Read more
A new family of limited-memory variationally-derived variable metric or quasi-Newton methods for unconstrained minimization is given. The methods have quadratic termination property and use updates, invariant under linear transformations. Some encouraging numerical experience is reported. CitationTechnical Report V-973. Prague, ICS AS CR 2006.ArticleDownload View PDF
In this paper we review the different tractable approximations of individual chance constraint problems using robust optimization on a varieties of uncertainty set, and show their interesting connections with bounds on the condition-value-at-risk CVaR measure popularized by Rockafellar and Uryasev. We also propose a new formulation for approximating joint chance constrained problems that improves upon … Read more
Inverse optimization perturbs objective function to make an initial feasible solution optimal with respect to perturbed objective function while minimizing cost of perturbation. We extend inverse optimization to two-stage stochastic linear programs. Since the resulting model grows with number of scenarios, we present two decomposition approaches for solving these problems. CitationUnpublished: 07-1, University of Pittsburgh, … Read more
This paper provides sufficient conditions for the optimal value function of a given linear semi-infinite programming problem to depend linearly on the size of the perturbations, when these perturbations are directional, involve either the cost coefficients or the right-hand-side function or both, and they are sufficiently small. Two kinds of partitions are considered. The first … Read more
When is the linear image of a closed convex cone closed? We present very simple, and intuitive necessary conditions, which 1) unify, and generalize seemingly disparate, classical sufficient conditions: polyhedrality of the cone, and “Slater” type conditions; 2) are necessary and sufficient, when the dual cone belongs to a class, that we call nice cones. … Read more