Related papers: Minimization Interchange Theorem on Posets
It is shown that optimal network plans can be obtained, naturally, as a limit of easier problems of point allocations. These problems are obtained by minimizing the mass transportation on the set of atomic measures of prescribed number of…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…
If a real-valued function is continuous on a real interval and it takes on two different values, then it will also take any value in between those two, by the Intermediate Value Theorem. It is not immediately clear what would be a natural…
We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{\'a}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four…
We design and mathematically analyze sampling-based algorithms for regularized loss minimization problems that are implementable in popular computational models for large data, in which the access to the data is restricted in some way. Our…
Given a probability measure over a state space, a partial collection (sub-$\sigma$-algebra) of events whose probabilities are known, induces a capacity over the collection of all possible events. The \emph{induced capacity} of an event $F$…
We address Nash equilibrium problems in a partial-decision information scenario, where each agent can only exchange information with some neighbors, while its cost function possibly depends on the strategies of all agents. We characterize…
The minimum number of inputs needed to control a network is frequently used to quantify its controllability. Control of linear dynamics through a minimum set of inputs, however, often has prohibitively large energy requirements and there is…
We propose a new approach for solving combinatorial optimization problem by utilizing the mechanism of chases and escapes, which has a long history in mathematics. In addition to the well-used steepest descent and neighboring search, we…
We consider the problem of minimizing a generalized relative entropy, with respect to a reference diffusion law, over the set of path-measures with fully prescribed marginal distributions. When dealing with the actual relative entropy,…
The exchange algorithm is one of the most popular extensions of the Metropolis--Hastings algorithm to sample from doubly-intractable distributions. However, the theoretical exploration of the exchange algorithm is very limited. For example,…
There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very…
Modern applications require robots to comply with multiple, often conflicting rules and to interact with the other agents. We present Posetal Games as a class of games in which each player expresses a preference over the outcomes via a…
In sorting literature, comparative statics for multidimensional assignment models with general output functions and input distributions is an important open question. We provide a complete theory of comparative statics for technological…
The transmission switching problem aims to determine the optimal network topology that minimizes the operating costs of a power system. This problem is typically formulated as a mixed-integer optimization model, which involves big-M…
We consider the problem of selecting a minimum size subset of nodes in a network, that allows to activate all the nodes of the network. We present a fast and simple algorithm that, in real-life networks, produces solutions that outperform…
In this work, we propose a new lecture of input-output model reconciliation Markov chain and the dominance theory, in the field of interindustrial poles interactions. A deeper lecture of Leontieff table in term of Markov chain is given,…