Related papers: Prophet Inequalities via Linear Programming
We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid…
The classical linear ordering problem seeks a single ranking representing a given preference matrix. While suitable for homogeneous populations, it fails when observed preferences arise from several latent groups with distinct ranking…
For each positive integer $n \geq 4$, we give an inequality satisfied by rank functions of arrangements of $n$ subspaces. When $n=4$ we recover Ingleton's inequality; for higher $n$ the inequalities are all new. These inequalities can be…
In this paper we investigate the potential for persuasion arising from the quantum indeterminacy of a decision-maker's beliefs, a feature that has been proposed as a formal expression of well-known cognitive limitations. We focus on a…
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…
Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known…
While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the properties that optimal solutions need to have, and devised a…
In this paper, we study $k$-unit single sample prophet inequalities. A seller has $k$ identical, indivisible items to sell. A sequence of buyers arrive one-by-one, with each buyer's private value for the item, $X_i$, revealed to the seller…
Let a polyhedral convex set be given by a finite number of linear inequalities and consider the problem to project this set onto a subspace. This problem, called polyhedral projection problem, is shown to be equivalent to multiple objective…
We consider the classical online bipartite matching problem in the probe-commit model. In this problem, when an online vertex arrives, its edges must be probed to determine if they exist, based on known edge probabilities. A probing…
This paper presents new existence, dual representation, and approximation results for the information projection in the infinite-dimensional setting for moment inequality models. These results are established under a general specification…
We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.
A typical bottleneck of model predictive control algorithms is the computational burden in order to compute the receding horizon feedback law which is predominantly determined by the length of the prediction horizon. Based on a relaxed…
The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…
We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
In this paper, we present a novel method for computing the asymptotic values of both the optimal threshold, and the probability of success in sequences of optimal stopping problems. This method, based on the resolution of a first-order…
In this paper, we solve explicitly the optimal stopping problem with random discounting and an additive functional as cost of observations for a regular linear diffusion. We also extend the results to the class of one-sided regular Feller…
This paper studies the fundamental limits of availability and throughput for independent and heterogeneous demands of a limited resource. Availability is the probability that the demands are below the capacity of the resource. Throughput is…
The simplex method in Linear Programming motivates several problems of asymptotic convex geometry. We discuss some conjectures and known results in two related directions -- computing the size of projections of high dimensional polytopes…