arXiv subjects

Imad Jaimoukha

Publications and source records attributed to Imad Jaimoukha.

3 recordsLinked to original sources

arXiv2025

First and Second Order Optimal $\mathcal{H}_2$ Model Reduction for Linear Continuous-Time Systems

In this paper, we investigate the optimal $\mathcal{H}_2$ model reduction problem for single-input single-output (SISO) continuous-time linear time-invariant (LTI) systems. A semi-definite relaxation (SDR) approach is proposed to determine globally optimal interpolation points, providing an effective way to compute the reduced-order models via Krylov projection-based methods. In contrast to iterative approaches, we use the controllability Gramian and the moment-matching conditions to recast the model reduction problem as a convex optimization by introducing an upper bound $\gamma$ to minimize the $\mathcal{H}_2$ norm of the model reduction error system. We also prove that the relaxation is exact for first order reduced models and demonstrate, through examples, that it is exact for second order reduced models. We compare the performance of our proposed method with other iterative approaches and shift-selection methods on examples. Importantly, our approach also provides a means to verify the global optimality of known locally convergent methods.

math.OC↗

arXiv2023

Fair and skill-diverse student group formation via constrained k-way graph partitioning

Forming the right combination of students in a group promises to enable a powerful and effective environment for learning and collaboration. However, defining a group of students is a complex task which has to satisfy multiple constraints. This work introduces an unsupervised algorithm for fair and skill-diverse student group formation. This is achieved by taking account of student course marks and sensitive attributes provided by the education office. The skill sets of students are determined using unsupervised dimensionality reduction of course mark data via the Laplacian eigenmap. The problem is formulated as a constrained graph partitioning problem, whereby the diversity of skill sets in each group are maximised, group sizes are upper and lower bounded according to available resources, and `balance' of a sensitive attribute is lower bounded to enforce fairness in group formation. This optimisation problem is solved using integer programming and its effectiveness is demonstrated on a dataset of student course marks from Imperial College London.

cs.LG↗

arXiv2022

Meta-learning based Alternating Minimization Algorithm for Non-convex Optimization

In this paper, we propose a novel solution for non-convex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of sub-problems corresponding to each variable, and then iteratively optimize each sub-problem using a fixed updating rule. However, due to the intrinsic non-convexity of the original optimization problem, the optimization can usually be trapped into spurious local minimum even when each sub-problem can be optimally solved at each iteration. Meanwhile, learning-based approaches, such as deep unfolding algorithms, are highly limited by the lack of labelled data and restricted explainability. To tackle these issues, we propose a meta-learning based alternating minimization (MLAM) method, which aims to minimize a partial of the global losses over iterations instead of carrying minimization on each sub-problem, and it tends to learn an adaptive strategy to replace the handcrafted counterpart resulting in advance on superior performance. Meanwhile, the proposed MLAM still maintains the original algorithmic principle, which contributes to a better interpretability. We evaluate the proposed method on two representative problems, namely, bi-linear inverse problem: matrix completion, and non-linear problem: Gaussian mixture models. The experimental results validate that our proposed approach outperforms AM-based methods in standard settings, and is able to achieve effective optimization in challenging cases while other comparing methods would typically fail.

cs.LG↗