We introduce generalizations of stochastic network interdiction problem with distributional ambiguity. Specifically, we consider a distributionally risk-averse (or robust) (DRA-NIP) and risk-receptive (DRR-NIP) where leader maximizes follower's minimal expected objective value for either the worst-case or best-case, respectively, probability distribution belonging to ambiguity set (a distributi...

In this paper we discuss a CSG BSP algorithm to perform the conversion from the boundary to the interior of d dimensional polyhedra Both a d dimensional polyhedral point set and its boundary d faces are here represented as BSP trees In this approach no structure no ordering and even no orientation is required for such boundary BSP trees In particular it is shown that the interior point set may ...

Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex sets. We propose a class of algorithms that perform both stochastic gradient descent and random feasibility updates simultaneously. At every iteration, the alg...

We develop a modular and tractable framework for solving a distributionally adaptive optimization problem, where we minimize the worst-case expected cost over an ambiguity set of probability distributions. The adaptive optimization framework caters for dynamic decision making, where decisions can adapt to the uncertain outcomes as they unfold in stages. We propose a second-order conic (SOC) rep...

Minimizing a nondecreasing separable concave cost function over a polyhedral set arises in capacity planning problems where economies of scale and fixed costs are significant, as well as production planning when a learning effect results in decreasing marginal costs. This is an NP-hard combinatorial problem in which the extreme points of the polyhedral set must be enumerated, each of them a loc...

Beyond perfection, the field to be explored is too wide. In this context, several ways to classify imperfect graphs or, equivalently, 0, 1 (clique-node) imperfect matrices can be found in the literature. From the polyhedral point of view, ideal matrices are to set covering problems what perfect matrices are to set packing problems. In fact, if a matrix is ideal, its linear relaxation is an inte...

We present a model for the vehicle and crew scheduling problem in urban public transport systems by combining models for vehicle and crew scheduling that cover a great variety of real world aspects, especially constraints for crews resulting from wage agreements and internal regulations. The main part of the model consists of a set partitioning formulation to cover the desired trips of the sche...

We introduce the framework of polyhedral branching systems that can be used in order to construct extended formulations for polyhedra by combining extended formulations for other polyhedra. The framework, for instance, simultaneously generalizes extended formulations like the well-known ones (see Balas [1]) for the convex hulls of unions of polyhedra (disjunctive programming) and like those obt...

We consider a distributionally robust optimization problem where the ambiguity set of probability distributions is characterized by a tractable conic representable support set and expectation constraints. Specifically, we propose and motivate a new class of infinitely constrained ambiguity sets in which the number of expectation constraints could potentially be infinite. We show how the infinit...

In this paper we discuss a CSG/BSP algorithm to perform the conversion from the boundary to the interior of d-dimensional polyhedra. Both a d-dimensional polyhedral point-set and its boundary (d 1)-faces are here represented as BSP trees. In this approach no structure, no ordering and even no orientation is required for such boundary BSP trees. In particular it is shown that the interior point-...