Using Hiriart-Urruty’s signed distance function, we present new definitions of strong slopes for a vector-valued map recently introduced in [E.M. Bednarczuk, A.Y., Kruger, Error bounds for vector-valued functions on metric spaces. Vietnam J. Math. 40 (2012), no. 2-3, 165-180]. With the new presentation, we are able to show that these slopes enjoy most properties of … Read more
This paper addresses combined location/routing problems defined on trees. Several problems are studied, which consider service demand both at the vertices and the edges of the input tree. Greedy type optimal heuristics are presented for the cases when all vertices have to be visited and facilities have no set-up costs. Facilities set-up costs can also … Read more
We consider the problem of minimizing a Lipschitz differentiable function over a class of sparse symmetric sets that has wide applications in engineering and science. For this problem, it is known that any accumulation point of the classical projected gradient (PG) method with a constant stepsize $1/L$ satisfies the $L$-stationarity optimality condition that was introduced … Read more
We study the polyhedron of the unit commitment problem, and consider a relaxation involving the ramping constraints. We study the three-period ramp-up polytope, and describe the convex-hull using a new class of inequalities. Citation [1] J. Ostrowski, M. F. Anjos, and A. Vannelli, \Tight mixed integer linear programming formulations for the unit commitment problem,” Power … Read more
Exploiting sparsity in Semidefinite Programs (SDP) is critical to solving large-scale problems. The chordal completion based maximal clique decomposition is the preferred approach for exploiting sparsity in SDPs. In this paper, we show that the maximal clique-based SDP decomposition is primal degenerate when the SDP has a low rank solution. We also derive conditions under … Read more
The automated real time control of an electrical network is achieved through the estimation of its state using Phasor Measurement Units (PMUs). Given an undirected graph representing the network, we study the problem of finding the minimum number of PMUs to place on the edges such that the graph is fully observed. This problem is … Read more
In this paper, we consider the control problem with the Average-Value-at-Risk (AVaR) criteria of the possibly unbounded $L^{1}$-costs in infinite horizon on a Markov Decision Process (MDP). With a suitable state aggregation and by choosing a priori a global variable $s$ heuristically, we show that there exist optimal policies for the infinite horizon problem. To … Read more
We consider an n-player finite strategic game. The payoff vector of each player is a random vector whose distribution is not completely known. We assume that the distribution of a random payoff vector of each player belongs to a distributional uncertainty set. We define a distributionally robust chance-constrained game using worst-case chance constraint. We consider … Read more
Stability analysis for optimization problems with chance constraints concerns impact of variation of probability measure in the chance constraints on the optimal value and optimal solutions and research on the topic has been well documented in the literature of stochastic programming. In this paper, we extend such analysis to optimization problems with distributionally robust chance … Read more
We study two-stage stochastic mixed integer programs (TSS-MIPs) with integer variables in the second stage. We show that under suitable conditions, the second stage MIPs can be convexified by adding parametric cuts a priori. As special cases, we extend the results of Miller and Wolsey (Math Program 98(1):73-88, 2003) to TSS-MIPs. Furthermore, we consider second … Read more