Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator

Categories Convex Optimization, Robust Optimization Tags , ,

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a p-dimensional Gaussian random vector from n independent samples. The proposed model minimizes the worst case (maximum) of Stein’s loss across all normal reference distributions within a prescribed Wasserstein distance from the normal distribution … Read more

A family of spectral gradient methods for optimization

Categories Convex Optimization, Unconstrained Optimization

We propose a family of spectral gradient methods, whose stepsize is determined by a convex combination of the short Barzilai-Borwein (BB) stepsize and the long BB stepsize. It is shown that each member of the family shares certain quasi-Newton property in the sense of least squares. The family also includes some other gradient methods as … Read more

Coalescing Data and Decision Sciences for Analytics

Categories Stochastic Programming Tags , ,

The dream of analytics is to work from common, clean, and consistent data sources in a manner that all of its facets (descriptive, predictive, and prescriptive) are sup- ported via a coherent vision of data and decision sciences. To the extent that data and decisions sciences work within logically/mathematically consistent frameworks, and that these paradigms … Read more

On decomposability of the multilinear polytope and its implications in mixed-integer nonlinear optimization

Categories (Mixed) Integer Nonlinear Programming, 0-1 Programming, Global Optimization Theory Tags , , ,

In this article, we provide an overview of some of our recent results on the facial structure of the multilinear polytope with a special focus on its decomposability properties. Namely, we demonstrate that, in the context of mixed-integer nonlinear optimization, the decomposability of the multilinear polytope plays a key role from both theoretical and algorithmic … Read more

Parallel and Distributed Successive Convex Approximation Methods for Big-Data Optimization

Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , ,

Recent years have witnessed a surge of interest in parallel and distributed optimization methods for large-scale systems. In particular, nonconvex large-scale optimization problems have found a wide range of applications in several engineering fields. The design and the analysis of such complex, large-scale, systems pose several challenges and call for the development of new optimization … Read more

The Synthesis Problem of Decentralized Energy Systems is strongly NP-hard

Categories Applications - Science and Engineering, Chemical Engineering, Combinatorial Optimization

We analyze the computational complexity of the synthesis problem of decentralized energy systems. This synthesis problem consists of combining various types of energy conversion units and determining their sizing as well as operations in order to meet time-varying energy demands while maximizing an objective function, e.g., the net present value. In this paper, we prove … Read more

Provably High-Quality Solutions for the Meal Delivery Routing Problem

Categories Integer Programming, Optimization of Systems modeled by PDEs, Transportation Tags , , , , ,

Online restaurant aggregators with integrated meal delivery networks have become more common and more popular in the past few years. Meal delivery is arguably the ultimate challenge in last mile logistics: a typical order is expected to be delivered within an hour (much less if possible), and within minutes of the food becoming ready. We … Read more

Stable interior point method for convex quadratic programming with strict error bounds

Categories Quadratic Programming Tags , , ,

We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown to have weak polynomial time complexity. A complete proof of the numerical stability of the method is provided. No … Read more

Optimal switching sequence for switched linear systems

Categories Combinatorial Optimization, Control Applications, Dynamic Programming Tags , , , , ,

We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of n-by-n matrices and an n-dimensional vector, find a sequence of K matrices, each chosen from the given set of matrices, to maximize a convex function over the product of the K matrices and the … Read more

Distributionally robust optimization with polynomial densities: theory, models and algorithms

Categories Robust Optimization, Semi-definite Programming Tags , , ,

In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A common shortcoming of most existing distributionally robust optimization models is that their ambiguity sets contain pathological discrete distribution that give nature too much … Read more