Positivstellensatz
WebThe Effective Positivstellensatz has also been studied for specific semi-algebraic sets, where special techniques can be applied to obtain better bounds: see for instance [LS21] for Schmüd-gen’s theorem on the unit box, [Slo21] for Schmüdgen’s theorem on the unit ball and simplex and [FF20] for Putinar’stheorem onthe unitsphere. WebBy exploiting Putinar positivstellensatz theorem [ 39 ], we formulate the mixed sensitivity controller design as the non-emptiness test of a convex set defined through a number of …
Positivstellensatz
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Webfirst proof of the Archimedean Positivstellensatz for compa ct semi-algebraic sets given in [S1] was essentially based on methods from functional analysis. The purpose of this … For certain sets S, there exist algebraic descriptions of all polynomials that are positive (resp. non-negative) on S. Such a description is a positivstellensatz (resp. nichtnegativstellensatz). The importance of Positivstellensatz theorems in computation arises from its ability to transform problems of polynomial optimization into semidefinite programming problems, which can be efficiently solved using convex optimization techniques.
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WebGiven linear matrix inequalities (LMIs) and it is natural to ask: WebSummary. We discuss (i) a quantized version of the Jordan decomposition theorem for a complex Borel measure on a compact Hausdorff space, namely, the more general problem of decomposing a general noncommutative kernel (a quantization of the standard notion of kernel function) as a linear combination of completely positive noncommutative kernels ...
Webfirst proof of the Archimedean Positivstellensatz for compa ct semi-algebraic sets given in [S1] was essentially based on methods from functional analysis. The purpose of this paper is to prove a strict Positivstellensatz for the Weyl algebra. Our approach uses again methods from operator theory and functional analysis. Let d∈ N.
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