Related papers: A Geometric Approach to Problems in Optimization a…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…
Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…
The problem of finding the densest subgraph in a given graph has several applications in graph mining, particularly in areas like social network analysis, protein and gene analyses etc. Depending on the application, finding dense subgraphs…
Recent results in homotopy and solution paths demonstrate that certain well-designed greedy algorithms, with a range of values of the algorithmic parameter, can provide solution paths to a sequence of convex optimization problems. On the…
We propose a data-driven method to establish probabilistic performance guarantees for parametric optimization problems solved via iterative algorithms. Our approach addresses two key challenges: providing convergence guarantees to…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of…
We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
Data-driven algorithm selection is a powerful approach for choosing effective heuristics for computational problems. It operates by evaluating a set of candidate algorithms on a collection of representative training instances and selecting…
This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…
We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which maximise the number of inliers-- this approach efficiently searches for a soft assignment of points to models by…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…
In the first part of this paper, we present a unified framework for analyzing the algorithmic complexity of any optimization problem, whether it be continuous or discrete in nature. This helps to formalize notions like "input", "size" and…