Výsledky vyhledávání - "Dunbar, Alex"

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Autor: Blekherman, Grigoriy, Dunbar, Alex, Sinn, Rainer

We study the Pythagoras numbers $py(3,2d)$ of real ternary forms, defined for each degree $2d$ as the minimal number $r$ such that every degree $2d$ ternary form which is a sum of squares can be written as the sum of at most $r$ squares of degree $d$

Externí odkaz: http://arxiv.org/abs/2410.17123

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A Topological Approach to Simple Descriptions of Convex Hulls of Sets Defined by Three Quadrics

Autor: Blekherman, Grigoriy, Dunbar, Alex

We study the convex hull of a set $S\subset \mathbb{R}^n$ defined by three quadratic inequalities. A simple way of generating inequalities valid on $S$ is to take nonnegative linear combinations of the defining inequalities of $S$. We call such inequ

Externí odkaz: http://arxiv.org/abs/2405.18282

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Relaxations and Duality for Multiobjective Integer Programming

Autor: Dunbar, Alex, Sinha, Saumya, Schaefer, Andrew J

Multiobjective integer programs (MOIPs) simultaneously optimize multiple objective functions over a set of linear constraints and integer variables. In this paper, we present continuous, convex hull and Lagrangian relaxations for MOIPs and examine th

Externí odkaz: http://arxiv.org/abs/2309.08801

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Alternating Minimization for Regression with Tropical Rational Functions

Autor: Dunbar, Alex, Ruthotto, Lars

Publikováno v: Alg. Stat. 15 (2024) 85-111

We propose an alternating minimization heuristic for regression over the space of tropical rational functions with fixed exponents. The method alternates between fitting the numerator and denominator terms via tropical polynomial regression, which is

Externí odkaz: http://arxiv.org/abs/2305.20072

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