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In the d-Euclidean Distance Matrix Completion (d-EDMC) problem, one aims to determine whether a given partial matrix of pairwise distances can be extended to a full Euclidean distance matrix in d dimensions. This problem is a cornerstone of…
The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness. Penner…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
Distance metric learning can be viewed as one of the fundamental interests in pattern recognition and machine learning, which plays a pivotal role in the performance of many learning methods. One of the effective methods in learning such a…
This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…
The Distance Geometry Problem asks for a realization of a given weighted graph in $\mathbb{R}^K$. Two variants of this problem, both originating from protein conformation, are based on a given vertex order (which abstracts the protein…
Coupled 3D-1D problems arise in many practical applications, in an attempt to reduce the computational burden in simulations where cylindrical inclusions with a small section are embedded in a much larger domain. Nonetheless the resolution…
The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent $x$ belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
In this paper we present a new semidefinite programming hierarchy for covering problems in compact metric spaces. Over the last years, these kind of hierarchies were developed primarily for geometric packing and for energy minimization…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…
We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…
This paper proposes concentrated geo-privacy (CGP), a privacy notion that can be considered as the counterpart of concentrated differential privacy (CDP) for geometric data. Compared with the previous notion of geo-privacy [ABCP13, CABP13],…
Molecular representation pretraining is critical in various applications for drug and material discovery due to the limited number of labeled molecules, and most existing work focuses on pretraining on 2D molecular graphs. However, the…
This paper introduces a novel Differential Dynamic Programming (DDP) algorithm for solving discrete-time finite-horizon optimal control problems with inequality constraints. Two variants, namely Feasible- and Infeasible-IPDDP algorithms,…