Convex Analysis: Theory and
                    Applications

Magaril-Il'yaev, Georgii Georgievich; Тихомиров, В. М.

doi:10.1090/mmono/222

Cited by 62 publications

(31 citation statements)

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“…(c) If there is a point A i ∈ {A 1 , A 2 , A 3 , A 4 } satisfying G. G. Magaril-ll'yaev and V. M. Tikhomirov note that no construction of the weighted Fermat-Torricelli point with ruler and compass is known for a simplex with n + 1 vertices in R n [6,Subsection 8.4,p. 96].…”

Section: )mentioning

confidence: 99%

The weighted Fermat–Torricelli–Menger problem for a given sextuple of edge lengths determining tetrahedra

Zachos

2016

J Math Chem

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We introduce the weighted Fermat-Torricelli-Menger problem for a given sextuple of edge lengths in R 3 which states that: given a sextuple of edge lengths determining tetrahedra and a positive real number (weight) which corresponds to each vertex of every derived tetrahedron find the corresponding weighted Fermat-Torricelli point of these tetrahedra. We obtain a system of three rational equations with respect to three variable distances from the weighted Fermat-Torricelli point to the three vertices of the tetrahedron determined by a given sextuple of edge lengths in the sense of Menger. This system of equations gives a necessary condition to locate the weighted Fermat-Torricelli point at the interior of this class of tetrahedra and allow us to compute the position of the corresponding weighted Fermat-Torricelli point. Furthermore, we give an analytical solution for the weighted Fermat-Torricelli-Menger problem for a given sextuple of equal edge lengths in R 3 for the case of two pairs of equal weights.

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Section: )mentioning

confidence: 99%

The weighted Fermat–Torricelli–Menger problem for a given sextuple of edge lengths determining tetrahedra

Zachos

2016

J Math Chem

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“…is the convex closure [30] of the output entropy H ( (ρ)) 3 . The functionĤ (ρ) is a natural generalization of another important quantity in quantum information theory, namely the "entanglement of formation" [6] and reduces to it when the channel is a partial trace.…”

Section: A Hierarchy Of the Additivity Conjecturesmentioning

confidence: 99%

The additivity problem in quantum information theory

Holevo¹

2007

Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006

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“…15 Thus, in everything that follows we consider only solutions to the reduced contract-design problem that satisfy ∆(x) = 0 without having to impose this condition as an extra constraint in the search for a 15 Note that δ = −∆(x) satisfies (13) as a direct consequence of (12).…”

Section: The Reduced Contract-design Problemmentioning

confidence: 99%

Efficient Contract Design in Multi-Principal Multi-Agent Supply Chains

Weber

Xiong

2006

SSRN Journal

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We consider a general multi-principal multi-agent contracting game in a complete-information supply-chain setting and determine coordinating equilibrium transfer schedules in closed form. The resulting contracts manage to align incentives for decentralized decision-making and achieve first-best channel solutions. We allow for multidimensional actions and arbitrary payoff externalities between all members of the supply chain. For the coordinating contracts to exist it suffices that all payoff functions are continuous on the compact action sets in a general sense that accommodates discrete action sets. Our approach unifies and generalizes a significant portion of the extant supply-chain literature. It can be applied to a very large class of many-to-many supply-chain settings.

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Convex Analysis: Theory and Applications

Cited by 62 publications

References 0 publications

The weighted Fermat–Torricelli–Menger problem for a given sextuple of edge lengths determining tetrahedra

The weighted Fermat–Torricelli–Menger problem for a given sextuple of edge lengths determining tetrahedra

The additivity problem in quantum information theory

Efficient Contract Design in Multi-Principal Multi-Agent Supply Chains

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