Chebyshev’s inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the unboundedness of the underlying support and are not considered realistic in many applications. We provide alternative tight lower … Read more
We propose a novel hub location model that jointly eliminates the traditional assumptions on the structure of the network and on the discount due to economies of scale in an effort to better reflect real-world logistics and transportation systems. Our model extends the hub literature in various facets: instead of connecting non-hub nodes directly to … Read more
Optimization of conflicting functions is of paramount importance in decision making, and real world applications frequently involve data that is uncertain or unknown, resulting in multi-objective optimization (MOO) problems of stochastic type. We study the stochastic multi-gradient (SMG) method, seen as an extension of the classical stochastic gradient method for single-objective optimization. At each iteration … Read more
In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate from the prospective of variational inequality. Preliminary numerical experiments on testing a sparse minimization problem from signal processing indicate that the proposed … Read more
Services must be delivered with high punctuality to be competitive. The classical scheduling theory offers to minimize the total earliness and tardiness of jobs to deliver punctual services. In this study, we developed a fully polynomial-time optimal algorithm to transform a given sequence, the permutation of jobs, into its corresponding minimum cost schedule, the timing … Read more
This paper is devoted to optimal control of dynamical systems governed by differential inclusions in both frameworks of Lipschitz continuous and discontinuous velocity mappings. The latter framework mostly concerns a new class of optimal control problems described by various versions of the so-called sweeping/Moreau processes that are very challenging mathematically and highly important in applications … Read more
We consider a two-player interdiction problem staged over a graph where the leader’s objective is to minimize the cost of removing edges from the graph so that the follower’s objective, i.e., the weight of a minimum spanning tree in the residual graph, is increased up to a predefined level $r$. Standard approaches for graph interdiction … Read more
We study a single-server appointment scheduling problem with a fixed sequence of appointments, for which we must determine the arrival time for each appointment. We specifically examine two stochastic models. In the first model, we assume that all appointees show up at the scheduled arrival times yet their service durations are random. In the second … Read more
We consider the embedding of piecewise-linear deep neural networks (ReLU networks) as surrogate models in mixed-integer linear programming (MILP) problems. A MILP formulation of ReLU networks has recently been applied by many authors to probe for various model properties subject to input bounds. The formulation is obtained by programming each ReLU operator with a binary … Read more
This paper continues the study of ‘good arrangements’ of collections of sets near a point in their intersection. Our aim is to clarify the relations between various quantitative geometric and metric characterizations of the transversality properties of collections of sets and the corresponding regularity properties of set-valued mappings. We expose all the parameters involved in … Read more