相关论文: A Gilmore-Gomory-Type Construction of Integer Prog…
A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and…
There are many applications where users seek to explore the impact of the settings of several categorical variables with respect to one dependent numerical variable. For example, a computer systems analyst might want to study how the type…
Symmetry in integer programs (IPs) can be exploited in order to reduce solving times. Usually only symmetries of the original IP are handled, but new symmetries may arise at some nodes of the branch-and-bound tree. While symmetry-handling…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
In a recent paper by Harada, Seceleanu, and \c{S}ega, the Hilbert function, betti table, and graded minimal free resolution of a general principal symmetric ideal are determined when the number of variables in the polynomial ring is…
We introduce a notion of integration defined from filters over families of finite sets. This procedure corresponds to determining the average value of functions whose range lies in any algebraic structure in which finite averages make…
We consider the quantum processor based on a chain of trapped ions to propose an architecture wherein the motional degrees of freedom of trapped ions (position and momentum) could be exploited as the computational Hilbert space. We adopt a…
Recently a class of generalized information measures was defined on sets of items parametrized by submodular functions. In this paper, we propose and study various notions of independence between sets with respect to such information…
We study existence and uniqueness of the fixed points solutions of a large class of non-linear variable discounted transfer operators associated to a sequential decision-making process. We establish regularity properties of these solutions,…
We first show a simple but striking result in bilevel optimization: unconstrained $C^\infty$ smooth bilevel programming is as hard as general extended-real-valued lower semicontinuous minimization. We then proceed to a worst-case analysis…
In this paper, a convex optimization-based method is proposed for numerically solving dynamic programs in continuous state and action spaces. The key idea is to approximate the output of the Bellman operator at a particular state by the…
Software products have become an integral part of human lives, and therefore need to account for human values such as privacy, fairness, and equality. Ignoring human values in software development leads to biases and violations of human…
Interval-valued computing is a relatively new computing paradigm. It uses finitely many interval segments over the unit interval in a computation as data structure. The satisfiability of Quantified Boolean formulae and other hard problems,…
We establish geometric and topological properties of the space of value functions in finite state-action Markov decision processes. Our main contribution is the characterization of the nature of its shape: a general polytope (Aigner et al.,…
Many operations related optimization problems involve repeatedly solving similar mixed integer linear programming (MILP) instances with the same constraint matrix but differing objective coefficients and right-hand-side values. The goal of…
This paper is concerned with the exact solution of mixed-integer programs (MIPs) over the rational numbers, i.e., without any roundoff errors and error tolerances. Here, one computational bottleneck that should be avoided whenever possible…
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…
Integer linear programs (ILPs) are commonly employed to model diverse practical problems such as scheduling and planning. Recently, machine learning techniques have been utilized to solve ILPs. A straightforward idea is to train a model via…
Optimization problems with set-valued objective functions arise in contexts such as multi-stage optimization with vector-valued objectives. The aim is to identify an optimizer -- a feasible point with an optimal objective value -- based on…
We present a fully nonparametric method to estimate the value function, via simulation, in the context of expected infinite-horizon discounted rewards for Markov chains. Estimating such value functions plays an important role in approximate…