In this article we address the problem of finding lower bounds for small Ramsey numbers $R(m,n)$ using circulant graphs. Our constructive approach is based on finding feasible colorings of circulant graphs using Integer Programming (IP) techniques. First we show how to model the problem as a Stackelberg game and, using the tools of bilevel optimization, … Read more
Limited-memory variable metric methods based on the well-known BFGS update are widely used for large scale optimization. The block version of the BFGS update, derived by Schnabel (1983), Hu and Storey (1991) and Vl·cek and Luk·san (2019), satis¯es the quasi-Newton equations with all used di®erence vectors and for quadratic objective functions gives the best improvement … Read more
Generation uncertainties, especially during the unit startup and shutdown (SU/SD) processes, pose uncertainties for the real-time market clearing process, and they are often underestimated. This paper proposes two approaches to predict generator SU/SD trajectories in the real-time operations of independent system operators or regional transmission organizations (ISO/RTOs). We first collect and pre-process raw market data … Read more
A wide class of problems involves the minimization of a coercive and differentiable function $F$ on $\mathbb{R}^N$ whose gradient cannot be evaluated in an exact manner. In such context, many existing convergence results from standard gradient-based optimization literature cannot be directly applied and robustness to errors in the gradient is not necessarily guaranteed. This work … Read more
In this work, we consider the integrated problem of locomotive scheduling and driver rostering in rail freight companies. Our aim is to compute an optimal simultaneous assignment of locomotives and drivers to the trains listed in a given order book. Mathematically, this leads to the combination of a set-packing problem with compatibility constraints and a … Read more
Nesterov’s accelerated gradient algorithm is derived from first principles. The first principles are founded on the recently-developed optimal control theory for optimization. The necessary conditions for optimal control generate a controllable dynamical system for accelerated optimization. Stabilizing this system via a control Lyapunov function generates an ordinary differential equation. An Euler discretization of the differential … Read more
The pandemic caused by the corona virus SARS-CoV-2 raised many new challenges for humanity. For instance, governments imposed regulations such as lockdowns, resulting in supply chain shocks at different tiers. Additionally, delivery services reached their capacity limits because the demand for mail orders soared temporarily during the lockdowns. We argue that one option to support … Read more
We consider the problem of learning an optimal prescriptive tree (i.e., an interpretable treatment assignment policy in the form of a binary tree) of moderate depth, from observational data. This problem arises in numerous socially important domains such as public health and personalized medicine, where interpretable and data-driven interventions are sought based on data gathered … Read more
We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is meant for a point to approximately solve the constraints, determining bounds on the expected number of iterations reduces to … Read more
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes bipartite graph matching and graph partitioning as special cases and is NP-hard, in general. We develop scalable linear … Read more