Related papers: Out-of-the-Box Global Optimization for Packing Pro…
In [1], the distributed linear-quadratic problem with fixed communication topology (DFT-LQ) and the sparse feedback LQ problem (SF-LQ) are formulated into a nonsmooth and nonconvex optimization problem with affine constraints. Moreover, a…
In this paper, we propose and analyze a multiscale method for a class of quasilinear elliptic problems of nonmonotone type with spatially multiscale coefficient. The numerical approach is inspired by the Localized Orthogonal Decomposition…
We present a nonlinear non-convex model predictive control approach to solving a real-world labyrinth game. We introduce adaptive nonlinear constraints, representing the non-convex obstacles within the labyrinth. Our method splits the…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
This work proposes a computational multiscale method for the mixed formulation of a second-order linear elliptic equation subject to a homogeneous Neumann boundary condition, based on a stable localized orthogonal decomposition (LOD) in…
While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
Intermodal logistics typically include the successive stages of intermodal shipment and last-mile delivery. We investigate this problem under a novel Logic-Based Benders Decomposition, which exploits the staged nature of the problem to…
We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our method subject to a verifiable geometric condition, which is…
It is commonly believed that the most efficient way to pack a finite number of equal-sized spheres is by arranging them tightly in a cluster. However, mathematicians have conjectured that a linear arrangement may actually result in the…
We tackle the problem of non-preemptive periodic scheduling with a harmonic set of periods. Problems of this kind arise within domains of periodic manufacturing and maintenance, and also during the design of industrial, automotive, and…
Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…
Recent transformer language models achieve outstanding results in many natural language processing (NLP) tasks. However, their enormous size often makes them impractical on memory-constrained devices, requiring practitioners to compress…
The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container so as to minimize a measure of overlap between ellipsoids is considered. A bilevel optimization formulation is given, together with an algorithm…
Many approaches for addressing Global Optimization problems typically rely on relaxations of nonlinear constraints over specific mathematical primitives. This is restricting in applications with constraints that are black-box, implicit or…
We study nonconvex optimization landscapes for learning overcomplete representations, including learning (i) sparsely used overcomplete dictionaries and (ii) convolutional dictionaries, where these unsupervised learning problems find many…
We give an overview of the 2024 Computational Geometry Challenge targeting the problem \textsc{Maximum Polygon Packing}: Given a convex region $P$ in the plane, and a collection of simple polygons $Q_1, \ldots, Q_n$, each $Q_i$ with a…
Following a polynomial approach, many robust fixed-order controller design problems can be formulated as optimization problems whose set of feasible solutions is modelled by parametrized polynomial matrix inequalities (PMI). These…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
We consider solving high-order semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new…