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The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
Achieving globally optimal point cloud registration under partial overlaps and large misalignments remains a fundamental challenge. While simultaneous transformation ($\boldsymbol{\theta}$) and correspondence ($\mathbf{P}$) estimation has…
A shape optimization problem arising from the optimal reinforcement of a membrane by means of one-dimensional stiffeners or from the fastest cooling of a two-dimensional object by means of ``conducting wires'' is considered. The criterion…
This paper considers phase retrieval from the magnitude of 1D over-sampled Fourier measurements, a classical problem that has challenged researchers in various fields of science and engineering. We show that an optimal vector in a…
Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
In this paper a phase-field approach for structural topology optimization for a 3D-printing process which includes stress constraint and potentially multiple materials or multiscales is analyzed. First order necessary optimality conditions…
Constructing well-behaved Laplacian and mass matrices is essential for tetrahedral mesh processing. Unfortunately, the \emph{de facto} standard linear finite elements exhibit bias on tetrahedralized regular grids, motivating the development…
The optimal design seeks the best possible solution(s) for a mechanical structure, device, or system, satisfying a series of requirements and leading to the best performance. In this work, optimized nozzle shapes have been designed for a…
We investigate approximation algorithms for several fundamental optimization problems on geometric packing. The geometric objects considered are very generic, namely $d$-dimensional convex fat objects. Our main contribution is a versatile…
This paper studies a two-material optimal design problem for the time-averaged duality pairing between a (possibly time-dependent) heat source and the weak solution of an initial-boundary value problem for the heat equation with a…
We consider the problem of finding a continuous and non-rigid matching between a 2D contour and a 3D mesh. While such problems can be solved to global optimality by finding a shortest path in the product graph between both shapes, existing…
In this paper, the problem of reaching formation for a network of rigid agents over a special orthogonal group is investigated by considering bearing-only constraints as the desired formation. Each agent is able to gather the measurements…
This paper studies a shape optimization problem which reduces to a nonlocal free boundary problem involving perimeter. It is motivated by a study of liquid crystal droplets with a tangential anchoring boundary condition and a volume…
We present filling as a new type of spatial subdivision problem that is related to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most…
This research addresses the increasing demand for advanced navigation systems capable of operating within confined surroundings. A significant challenge in this field is developing an efficient planning framework that can generalize across…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
A convex partition of a point set P in the plane is a planar partition of the convex hull of P with empty convex polygons or internal faces whose extreme points belong to P. In a convex partition, the union of the internal faces give the…