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Spectral methods provide an elegant and efficient way of numerically solving differential equations of all kinds. For smooth problems, truncation error for spectral methods vanishes exponentially in the infinity norm and $L_2$-norm.…
Two-stage stochastic programs become computationally challenging when the number of scenarios representing parameter uncertainties grows. Motivated by this, we propose the TULIP-algorithm ("Two-step warm start method Used for solving…
This paper considers the problem of distributed model fitting using the alternating directions method of multipliers (ADMM). ADMM splits the learning problem into several smaller subproblems, usually by partitioning the data samples. The…
This study investigates numerical methods to solve nonlinear transport problems characterized by various sorption isotherms with a focus on the Freundlich type of isotherms. We describe and compare second order accurate numerical schemes,…
We present two practical improvement techniques for unsupervised segmentation learning. These techniques address limitations in the resolution and accuracy of predicted segmentation maps of recent state-of-the-art methods. Firstly, we…
We propose adaptive, line search-free second-order methods with optimal rate of convergence for solving convex-concave min-max problems. By means of an adaptive step size, our algorithms feature a simple update rule that requires solving…
In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…
Cure models have been developed as an alternative modelling approach to conventional survival analysis in order to account for the presence of cured subjects that will never experience the event of interest. Mixture cure models, which model…
Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable…
One of the challenges in hyperspectral data analysis is the presence of mixed pixels. Mixed pixels are the result of low spatial resolution of hyperspectral sensors. Spectral unmixing methods decompose a mixed pixel into a set of endmembers…
We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…
Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…
Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…
The hyperspectral image (HSI) unmixing task is essentially an inverse problem, which is commonly solved by optimization algorithms under a predefined (non-)linear mixture model. Although these optimization algorithms show impressive…
The development of signal unmixing algorithms is essential for leveraging multimodal datasets acquired through a wide array of scientific imaging technologies, including hyperspectral or time-resolved acquisitions. In experimental physics,…
Alternating minimization methods have recently been proposed as alternatives to the gradient descent for deep neural network optimization. Alternating minimization methods can typically decompose a deep neural network into layerwise…
We introduce a constrained optimization framework for training transformers that behave like optimization descent algorithms. Specifically, we enforce layerwise descent constraints on the objective function and replace standard empirical…
We consider robust submodular maximization problems (RSMs), where given a set of $m$ monotone submodular objective functions, the robustness is with respect to the worst-case (scaled) objective function. The model we consider generalizes…
We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…
The deployment of large language models (LLMs) is largely hindered by their large number of parameters. Structural pruning has emerged as a promising solution. Prior structured pruning methods directly remove unimportant parameters based on…