Error Analysis

Luo, Zhi-Quan; Sturm, J.F.

doi:10.1007/978-1-4615-4381-7_7

Cited by 7 publications

(1 citation statement)

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“…Any method of obtaining finite certificates of infeasibility can be used in place of RD, as long as it takes polynomial time to verify them. See the comments after Theorem 3.5 in Sturm [24] and also Theorem 7.5.1 of [12] for another certificate of infeasibility. Klep and Schweighofer [6] also developed certificates for infeasibility and a hierarchy of infeasibility in which 0-infeasibility corresponds to strong infeasibility and k-infeasibility to weak infeasibility, when k > 0.…”

Section: C) Is Feasible If and Only If Rd(k N L C) Is Infeasiblementioning

confidence: 99%

A Structural Geometrical Analysis of Weakly Infeasible SDPS

Lourenço

Muramatsu

Tsuchiya

2016

JORSJ

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In this article, we develop a detailed analysis of semidefinite feasibility problems (SDFPs) to understand how weak infeasibility arises in semidefinite programming. This is done by decomposing a SDFP into smaller problems, in a way that preserves most feasibility properties of the original problem. The decomposition utilizes a set of vectors (computed in the primal space) which arises when we apply the facial reduction algorithm to the dual feasible region. In particular, we show that for a weakly infeasible problem over n × n matrices, at most n − 1 directions are required to approach the positive semidefinite cone. We also present a discussion on feasibility certificates for SDFPs and related complexity results.

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Section: C) Is Feasible If and Only If Rd(k N L C) Is Infeasiblementioning

confidence: 99%

A Structural Geometrical Analysis of Weakly Infeasible SDPS

Lourenço

Muramatsu

Tsuchiya

2016

JORSJ

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Precision measurement and compensation of kinematic errors for industrial robots using artifact and machine learning

2022

Adv. Manuf.

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Blind constant modulus equalization via convex optimization

Mariere

Luo

Davidson

2003

IEEE Trans. Signal Process.

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In this paper, we formulate the problem of blind equalization of constant modulus (CM) signals as a convex optimization problem. The convex formulation is obtained by performing an algebraic transformation on the direct formulation of the CM equalization problem. Using this transformation, the original nonconvex CM equalization formulation is turned into a convex semidefinite program (SDP) that can be efficiently solved using interior point methods. Our SDP formulation is applicable to baud spaced equalization as well as fractionally spaced equalization. Performance analysis shows that the expected distance between the equalizer obtained by the SDP approach and the optimal equalizer in the noise-free case converges to zero exponentially as the signal-to-noise ratio (SNR) increases. In addition, simulations suggest that our method performs better than standard methods while requiring significantly fewer data samples.

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Error Analysis

Cited by 7 publications

References 0 publications

A Structural Geometrical Analysis of Weakly Infeasible SDPS

A Structural Geometrical Analysis of Weakly Infeasible SDPS

Precision measurement and compensation of kinematic errors for industrial robots using artifact and machine learning

Blind constant modulus equalization via convex optimization

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