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
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
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
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
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
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
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
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
A robust-to-dynamics optimization (RDO) problem} is an optimization problem specified by two pieces of input: (i) a mathematical program (an objective function $f:\mathbb{R}^n\rightarrow\mathbb{R}$ and a feasible set $\Omega\subseteq\mathbb{R}^n$), and (ii) a dynamical system (a map $g:\mathbb{R}^n\rightarrow\mathbb{R}^n$). Its goal is to minimize $f$ over the set $\mathcal{S}\subseteq\Omega$ of initial conditions that forever remain in $\Omega$ under … Read more
The multilinear polytope MP_G of a hypergraph G is the convex hull of a set of binary points satisfying a collection of multilinear equations. We introduce the running-intersection inequalities, a new class of facet-defining inequalities for the multilinear polytope. Accordingly, we define a new polyhedral relaxation of MP_G referred to as the running-intersection relaxation and … Read more