Beginning in the 1960s, techniques from operations research began to be used to generate political districting plans. A classical example is the integer programming model of Hess et al. (Operations Research 13(6):998–1006, 1965). Due to the model’s compactness-seeking objective, it tends to generate contiguous or nearly-contiguous districts, although none of the model’s constraints explicitly impose … Read more
This paper studies a classic maximum entropy sampling problem (MESP), which aims to select the most informative principal submatrix with a given size out of a covariance matrix from a system. MESP has been widely applied to many areas, including healthcare, power system, manufacturing, data science, etc. Investigating its Lagrangian dual and primal characterization, we … Read more
The problem of finding global minima of nonlinear discrete functions arises in many fields of practical matters. In recent years, methods based on discrete filled functions become popular as ways of solving these sort of problems. However, they rely on the steepest descent method for local searches. Here we present an approach that does not … Read more
In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk. Focusing for the first time on the context where risk is measured according to convex risk measures, we … Read more
This paper continues the study of general nonlinear transversality properties of collections of sets and focuses on primal space necessary (in some cases also sufficient) characterizations of the properties. We formulate geometric, metric and slope characterizations, particularly in the convex setting. The Holder case is given a special attention. Quantitative relations between the nonlinear transversality … Read more
As a result of its liberalization, the European gas market is organized as an entry-exit system in order to decouple the trading and transport of natural gas. Roughly summarized, the gas market organization consists of four subsequent stages. First, the transmission system operator (TSO) is obliged to allocate so-called maximal technical capacities for the nodes … Read more
A major difficulty in optimization with nonconvex constraints is to find feasible solutions. As simple examples show, the alphaBB-algorithm for single-objective optimization may fail to compute feasible solutions even though this algorithm is a popular method in global optimization. In this work, we introduce a filtering approach motivated by a multiobjective reformulation of the constrained … Read more
This paper proposes a scenario sampling-based framework to estimate the expected incremental routing cost required so as to incorporate a target customer into an inherently stochastic supply chain network. Inspired from a real-life setting arising in the distribution of industrial gases, we demonstrate our framework and elucidate the quality of the marginal cost estimates it … Read more
This paper studies an n-player non-cooperative game with strategy sets defined by stochastic linear constraints. The stochastic constraints of each player are jointly satisfied with a probability exceeding a given threshold. We consider the case where the row vectors defining the constraints are independent random vectors whose probability distributions are not completely known and belong … Read more
We investigate the unconstrained global optimization of functions with low effective dimensionality, that are constant along certain (unknown) linear subspaces. Extending the technique of random subspace embeddings in [Wang et al., Bayesian optimization in a billion dimensions via random embeddings. JAIR, 55(1): 361–387, 2016], we study a generic Random Embeddings for Global Optimization (REGO) framework … Read more