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In this research, we do a software writing in Python to calculate the efforts, bending moments and deformations in beams of different materials. This computational tool, that we developed, is of great help in area of computational physical,…
This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of…
We consider the task of reconstructing polytopes with fixed facet directions from finitely many support function evaluations. We show that for a fixed simplicial normal fan the least-squares estimate is given by a convex quadratic program.…
This article implements a simple convex approach and block techniques to obtain several new refined versions of numerical radius inequalities for Hilbert space operators. This includes comparisons among the norms of the operators, their…
The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. The support function can be used in order to approximate solutions to such problems by finite dimensional optimization…
Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optimization. We introduce the notion of a Lagrangian dual…
Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial…
Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial…
A quadratically constrained quadratic programming problem is considered in a Hilbert space setting, where neither the objective nor the constraint are convex functions. Necessary and sufficient conditions are provided to guarantee that the…
David Hilbert discovered in 1895 an important metric that is canonically associated to any convex domain $\Omega$ in the Euclidean (or projective) space. This metric is known to be Finslerian, and the usual proof assumes a certain degree of…
A new intrinsic volume metric is introduced for the class of convex bodies in $\mathbb{R}^n$. As an application, an inequality is proved for the asymptotic best approximation of the Euclidean unit ball by arbitrarily positioned polytopes…
Convex optimization is a well-established research area with applications in almost all fields. Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a…
Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can…
We construct a converging geometric iterated function system on the moduli space of ordered triangles, for which the involved functions have geometric meanings and contain a non-contraction map under the natural metric.
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…
Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…
We study the smallest intersecting and enclosing ball problems in Euclidean spaces for input objects that are compact and convex. They link and unify many problems in computational geometry and machine learning. We show that both problems…
The region of entropic vectors is a convex cone that has been shown to be at the core of many fundamental limits for problems in multiterminal data compression, network coding, and multimedia transmission. This cone has been shown to be…
We study translative integral formulas for certain translation invariant functionals on convex polytopes and discuss local extensions and applications to Poisson processes and Boolean models.
We consider the geometrization of quantum mechanics. We then focus on the pull-back of the Fubini-Study metric tensor field from the projective Hibert space to the orbits of the local unitary groups. An inner product on these tensor fields…