Maximizing concave piecewise affine functions on the unitary group

Gaubert, Stéphane; Qu, Zheng; Sridharan, Srinivas

doi:10.1007/s11590-015-0951-y

Optim Lett

2015

DOI: 10.1007/s11590-015-0951-y

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Maximizing concave piecewise affine functions on the unitary group

Stéphane Gaubert

Zheng Qu²,

Srinivas Sridharan

Abstract: International audienceWe show that a convex relaxation, introduced by Sridharan, McEneaney, Gu and James to approximate the value function of an optimal controlproblem arising from quantum gate synthesis, is exact. This relaxation appliesto the maximization of a class of concave piecewise affine functions over theunitary grou

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2020

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Cited by 2 publications

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“…+ − ; include a unitary matrix [3]. The Schröder's equation is a composition operator's eigenvalue equation C h , which presents a featuref to ( )…”

mentioning

confidence: 99%

Analysis of a Composition Operator’s Eigenvalue Equation on Unitary Spaces by the Krein-Rutman Theorem

Karim¹

2020

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The Krein-Rutman theorem is vital in partial differential equations that are non-linear and provides evidence of the presence of several significant eigenvalues useful in topological degree calculations, stability analysis, and bifurcation theory. Schröder's equation which has been used extensively in studies of turbulence is an equation with a single independent variable suitable for encoding self-similarity. The concept of Hilbert spaces has been an inner product space frequently used due to its convenience in countless dimensional vector analysis. This paper is aimed at proving a number of solutions through the Krein-Rutman theorem in unitary spaces especially in Hilbert spaces. It has been certainly observed that the whole Krein-Rutman theorem system has a fairly stable scope, and has strong regular features, and many non-linear elliptic operators need the most ethical principles to satisfy the comparison policy.

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“…+ − ; include a unitary matrix [3]. The Schröder's equation is a composition operator's eigenvalue equation C h , which presents a featuref to ( )…”

mentioning

confidence: 99%

Analysis of a Composition Operator’s Eigenvalue Equation on Unitary Spaces by the Krein-Rutman Theorem

Karim¹

2020

View full text Add to dashboard Cite

show abstract

Analysis of a Composition Operator’s Eigenvalue Equation on Unitary Spaces by the Krein-Rutman Theorem

Karim¹

2020

View full text Add to dashboard Cite

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Maximizing concave piecewise affine functions on the unitary group

Cited by 2 publications

References 14 publications

Analysis of a Composition Operator’s Eigenvalue Equation on Unitary Spaces by the Krein-Rutman Theorem

Analysis of a Composition Operator’s Eigenvalue Equation on Unitary Spaces by the Krein-Rutman Theorem

Analysis of a Composition Operator’s Eigenvalue Equation on Unitary Spaces by the Krein-Rutman Theorem

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