We present a linear cutting-plane relaxation approach that rapidly proves tight lower bounds for the Alternating Current Optimal Power Flow Problem (ACOPF). Our method leverages outer-envelope linear cuts for well-known second-order cone relaxations for ACOPF along with modern cut management techniques. These techniques prove effective on a broad family of ACOPF instances, including the largest … Read more
The worldwide citrus market has been impacted by various factors in recent years, including population growth, phytosanitary diseases, high costs of agricultural inputs, and diminishing planting areas. As a consequence, producers in this sector have attempted to find tools to support strategic planting decisions, and thus meet international contract demands. This paper proposes an optimization … Read more
We consider the complex cut polytope: the convex hull of Hermitian rank 1 matrices \(xx^{\mathrm{H}}\), where the elements of \(x \in \mathbb{C}^n\) are \(m\)th unit roots. These polytopes have applications in \({\text{MAX-3-CUT}}\), digital communication technology, angular synchronization and more generally, complex quadratic programming. For \({m=2}\), the complex cut polytope corresponds to the well-known cut polytope. … Read more
Nonconvex, nonlinear cost functions arise naturally in physical inverse problems and machine learning. The alternating direction method of multipliers (ADMM) has seen extensive use in these applications, despite exhibiting uncertain convergence behavior in many practical nonconvex settings, and struggling with general nonlinear constraints. In contrast, filter methods have proved effective in enforcing convergence for sequential … Read more
In this work, we consider the bilevel optimization problem on Riemannian manifolds. We inspect the calculation of the hypergradient of such problems on general manifolds and thus enable the utilization of gradient-based algorithms to solve such problems. The calculation of the hypergradient requires utilizing the notion of Riemannian cross-derivative and we inspect the properties and … Read more
Omnichannel services, such as buy-online-pickup-in-store, curbside pickup, and ship-from-store, have shifted the order-picking tasks previously completed by in-store customers doing their own shopping to the retailer’s responsibility. To fulfill these orders, many retailers have deployed a store fulfillment strategy, where online orders are picked from brick-and-mortar retail store shelves. We focus on the design of … Read more
In this paper, we consider copositive cones over symmetric cones and show that they are never facially exposed when the underlying cone has dimension at least 2. We do so by explicitly exhibiting a non-exposed extreme ray. Our result extends the known fact that the cone of copositive matrices over the nonnegative orthant is not … Read more
A traditional stochastic program under a finite population typically seeks to optimize efficiency by maximizing the expected profits or minimizing the expected costs, subject to a set of constraints. However, implementing such optimization-based decisions can have varying impacts on individuals, and when assessed using the individuals’ utility functions, these impacts may differ substantially across demographic … Read more
In a previous work, we introduced a new linear programming (LP) relaxation for K-means clustering. In this paper, we further investigate the theoretical properties of this relaxation. We focus on K-means clustering with two clusters, which is an NP-hard problem. As evident from our numerical experiments with both synthetic and real-world data sets, the proposed … Read more
The length-constrained cycle partition problem (LCCP) is a graph optimization problem in which a set of nodes must be partitioned into a minimum number of cycles. Every node is associated with a critical time and the length of every cycle must not exceed the critical time of any node in the cycle. We formulate LCCP … Read more