Robust convex constraints are difficult to handle, since finding the worst-case scenario is equivalent to maximizing a convex function. In this paper, we propose a new approach to deal with such constraints that unifies approaches known in the literature and extends them in a significant way. The extension is either obtaining better solutions than the … Read more
We study the problem of online learning (OL) from revealed preferences: a learner wishes to learn an agent’s private utility function through observing the agent’s utility-maximizing actions in a changing environment. We adopt an online inverse optimization setup, where the learner observes a stream of agent’s actions in an online fashion and the learning performance … Read more
The analysis of projection-free first order methods is often complicated by the presence of different kinds of “good” and “bad” steps. In this article, we propose a unifying framework for projection-free methods, aiming to simplify the converge analysis by getting rid of such a distinction between steps. The main tool employed in our framework is … Read more
Over the last two decades, coherent risk measures have been well studied as a principled, axiomatic way to measure the risk of a random variable. Because of this axiomatic approach, coherent risk measures have a number of attractive features for computation, and they have been integrated into a variety of stochastic programming algorithms, including stochastic … Read more
We present a mathematical and computational framework for the problem of learning a dynamical system from noisy observations of a few trajectories and subject to side information. Side information is any knowledge we might have about the dynamical system we would like to learn besides trajectory data. It is typically inferred from domain-specific knowledge or … Read more
We consider the problem of optimal placement of concentrated masses along a massless elastic column that is clamped at one end and loaded by a nonconservative follower force at the free end. The goal is to find the largest possible interval such that the variation in the loading parameter within this interval preserves stability of … Read more
Given a graph G and an interdiction budget k, the Edge Interdiction Clique Problem (EICP) asks to find a subset of at most k edges to remove from G so that the size of the maximum clique, in the interdicted graph, is minimized. The EICP belongs to the family of interdiction problems with the aim … Read more
We utilize association schemes to analyze the quality of semidefinite programming (SDP) based convex relaxations of integral packing and covering polyhedra determined by matchings in hypergraphs. As a by-product of our approach, we obtain bounds on the clique and stability numbers of some regular graphs reminiscent of classical bounds by Delsarte and Hoffman. We determine … Read more
The European gas market is implemented as an entry-exit system, which aims to decouple transport and trading of gas. It has been modeled in the literature as a multilevel problem, which contains a nonlinear flow model of gas physics. Besides the multilevel structure and the nonlinear flow model, the computation of so-called technical capacities is … Read more
We consider the notions of (i) critical points, (ii) second-order points, (iii) local minima, and (iv) strict local minima for multivariate polynomials. For each type of point, and as a function of the degree of the polynomial, we study the complexity of deciding (1) if a given point is of that type, and (2) if … Read more