Related papers: Comparing Parameterizations and Objective Function…
The prevalence of variational methods in near-term quantum computing makes optimizer choice critical, yet selection is frequently intuition-based. We therefore present a systematic benchmark of eight classical optimization algorithms for…
We study the projection onto the set of feasible inputs and the set of feasible solutions of a polynomial optimisation problem (POP). Our motivation is increasing the robustness of solvers for POP: Without a priori guarantees of feasibility…
Computing mixed volume of convex polytopes is an important problem in computational algebraic geometry. This paper establishes sufficient conditions under which the mixed volume of several convex polytopes exactly equals the normalized…
Verification and synthesis of Cyber-Physical Systems (CPS) are challenging and still raise numerous issues so far. In this paper, based on a new concept of mixed sets defined as function images of symbol type domains, a compositional…
Qubit-efficient optimization studies how large combinatorial problems can be addressed with quantum circuits whose width is far smaller than the number of logical variables. In quadratic unconstrained binary optimization (QUBO), objective…
Metric magnitude is a measure of the "size" of point clouds with many desirable geometric properties. It has been adapted to various mathematical contexts and recent work suggests that it can enhance machine learning and optimization…
In this paper, we propose an efficient approach for the compression and representation of volumetric data utilizing coordinate-based networks and multi-resolution hash encoding. Efficient compression of volumetric data is crucial for…
The equations of motion of a mechanical system subjected to nonholonomic linear constraints can be formulated in terms of a linear almost Poisson structure in a vector bundle. We study the existence of invariant measures for the system in…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
Several large-scale machine learning tasks, such as data summarization, can be approached by maximizing functions that satisfy submodularity. These optimization problems often involve complex side constraints, imposed by the underlying…
An adaptation of Response Surface Methodology (RSM) when the covariate is of high or infinite dimensional is proposed, providing a tool for black-box optimization in this context. We combine dimension reduction techniques with classical…
In metabolomics, small molecules are structurally elucidated using tandem mass spectrometry (MS/MS); this resulted in the computational Maximum Colorful Subtree problem, which is NP-hard. Unfortunately, data from a single metabolite…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
In the case of multi-parameter full-waveform inversion, the computation of the additional Hessian terms that contain derivatives with respect to more than one type of parameter is necessary. If a simple gradient-based minimization is used,…
A strength of parameterized algorithmics is that each problem can be parameterized by an essentially inexhaustible set of parameters. Usually, the choice of the considered parameter is informed by the theoretical relations between…
We provide a systematic deterministic numerical scheme to approximate the volume (i.e. the Lebesgue measure) of a basic semi-algebraic set whose description follows a sparsity pattern. As in previous works (without sparsity), the underlying…
In this paper, we give a number of new exact algorithms and heuristics to compute linear boolean decompositions, and experimentally evaluate these algorithms. The experimental evaluation shows that significant improvements can be made with…
Convolution is an efficient technique to obtain abstract feature representations using hierarchical layers in deep networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other…
Reachability analysis for hybrid nonaffine systems remains computationally challenging, as existing set representations--including constrained, polynomial, and hybrid zonotopes--either lose tightness under high-order nonaffine maps or…
We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size ($n\lesssim 50$), and measure it on several state-of-the-art transmon devices, finding values…