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To broaden the range of applicability of variable-order fractional differential models, reliable numerical approaches are needed to solve the model equation. In this paper, we develop Laguerre spectral collocation methods for solving…
This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…
We, the QAIMS lab lab at the Aerospace Faculty of TU Delft, participated as finalists in the Airbus/BMW Quantum Computing Challenge 2024. Stacking sequence retrieval, a complex combinatorial task within a bi-level optimization framework, is…
In this paper, we introduce a model of a single-failure locally recoverable distributed storage system. This model appears to give rise to a problem seemingly dual of the well-studied index coding problem. The relation between the…
Much like classical supercomputers, scaling up quantum computers requires an optical interconnect. However, signal attenuation leads to irreversible qubit loss, making quantum interconnect design guidelines and metrics different from…
Quantum subspace diagonalization (QSD) algorithms have emerged as a competitive family of algorithms that avoid many of the optimization pitfalls associated with parameterized quantum circuit algorithms. While the vast majority of the QSD…
Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…
We study two-stage robust optimization problems with mixed discrete-continuous decisions in both stages. Despite their broad range of applications, these problems pose two fundamental challenges: (i) they constitute infinite-dimensional…
The Euclidean distance geometry problem arises in a wide variety of applications, from determining molecular conformations in computational chemistry to localization in sensor networks. When the distance information is incomplete, the…
We introduce two new methods for deterministic convex optimization problems: QCC (Quadratic Cuts for Convex optimization) and QB (Quadratic Bundle method). We prove the complexity of these methods for composite optimization problems which…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…
Motivated by studies of data retrieval in polymer-based storage systems, we consider the problem of reconstructing a multiset of binary strings that have the same length and the same weight from the compositions of their prefixes and…
A number of scientific fields rely on placing permanent magnets in order to produce a desired magnetic field. We have shown in recent work that the placement process can be formulated as sparse regression. However, binary, grid-aligned…
Multisite local orbitals, which are formed from linear combinations of pseudo-atomic orbitals from a target atom and its neighbor atoms, have been introduced in the large-scale density functional theory calculation code CONQUEST. Multisite…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…
A novel efficient and high accuracy numerical method for the time-fractional differential equations (TFDEs) is proposed in this work. We show the equivalence between TFDEs and the integer-order extended parametric differential equations…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
The interest in $q$-analogs of codes and designs has been increased in the last few years as a consequence of their new application in error-correction for random network coding. There are many interesting theoretical, algebraic, and…