Related papers: Starting CLuP with polytope relaxation
Clustering is a powerful and extensively used data science tool. While clustering is generally thought of as an unsupervised learning technique, there are also supervised variations such as Spath's clusterwise regression that attempt to…
Clustering techniques are consolidated as a powerful strategy for analyzing the extensive data generated from molecular modeling. In particular, some tools have been developed to cluster configurations from classical simulations with a…
In many classification problems it is desirable to output well-calibrated probabilities on the different classes. We propose a robust, non-parametric method of calibrating probabilities called SplineCalib that utilizes smoothing splines to…
This paper proposes a bilevel hierarchy of strengthened complex moment relaxations for complex polynomial optimization. The key trick entails considering a class of positive semidefinite conditions that arise naturally in characterizing the…
This paper introduces the 2019 version of \us{}, a novel Constraint Programming framework for floating point verification problems expressed with the SMT language of SMTLIB. SMT solvers decompose their task by delegating to specific…
Despite the strong reasoning capabilities of large language models (LLMs), optimizing the execution efficiency of tensor programs remains challenging due to the need for precise, composable transformation decisions. Recent LLM-guided…
The pooling problem is a classical NP-hard problem in the chemical process and petroleum industries. This problem is modeled as a nonlinear, nonconvex network flow problem in which raw materials with different specifications are blended in…
In this article, we develop a clique-based method for social network clustering. We introduce a new index to evaluate the quality of clustering results, and propose an efficient algorithm based on recursive bipartition to maximize an…
We present PLUTO, a powerful framework that pushes the limit of imitation learning-based planning for autonomous driving. Our improvements stem from three pivotal aspects: a longitudinal-lateral aware model architecture that enables…
With the aggressive scaling of VLSI technology, the explosion of layout patterns creates a critical bottleneck for DFM applications like OPC. Pattern clustering is essential to reduce data complexity, yet existing methods struggle with…
We analyse a general class of bilevel problems, in which the upper-level problem consists in the minimization of a smooth objective function and the lower-level problem is to find the fixed point of a smooth contraction map. This type of…
The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…
Navigating rigid body objects through crowded environments can be challenging, especially when narrow passages are presented. Existing sampling-based planners and optimization-based methods like mixed integer linear programming (MILP)…
Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However,…
Mixed-Integer Programming (MIP), particularly Mixed-Integer Linear Programming (MILP) and Mixed-Integer Quadratic Programming (MIQP), has found extensive applications in domains such as portfolio optimization and network flow control, which…
We present a novel relaxation framework for general mixed-integer nonlinear programming (MINLP) grounded in computational geometry. Our approach constructs polyhedral relaxations by convexifying finite sets of strategically chosen points,…
Fast and accurate large-scale energy system models are needed to investigate the potential of storage to complement the fluctuating energy production of renewable energy systems. However, standard Mixed-Integer Programming (MIP) models that…
Machine learning interatomic potentials (MLIPs) provide an effective approach for accurately and efficiently modeling atomic interactions, expanding the capabilities of atomistic simulations to complex systems. However, a priori feature…
Contrastive Language-Image Pre-training (CLIP) has become the standard for cross-modal image-text representation learning. Improving CLIP typically requires additional data and retraining with new loss functions, but these demands raise…
Trimmed (multi-patch) geometries are the state-of-the-art technology in computer-aided design for industrial applications such as automobile crashworthiness. In this context, fast solution techniques extensively rely on explicit time…