Interior-Point Algorithms for Semidefinite Programming Problems Derived from the KYP Lemma

Vandenberghe, Lieven; Balakrishnan, V.; Wallin, Ragnar; Hansson, Anders; Roh, Tae

doi:10.1007/10997703_12

Cited by 69 publications

(55 citation statements)

References 19 publications

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“…One way to utilize the lowrank property, when forming H, is to write a customized solver. This is explained in [20] and produces very good results. However, the code referenced in [20] does not detect if the SDP is infeasible.…”

Section: Further Improvements Of the Solvermentioning

confidence: 89%

“…This implies that the operator F has full rank, [20]. To see this we first notice that P will not change if we apply feedback,Ã = A − BL.…”

Section: Assumptionsmentioning

confidence: 98%

“…If we are only interested in the objective value we are ready, but if we want the primal variables P and x we have to reconstruct them. To this end we need the fact that the dual solution, X, of the above SDP is actually also a solution to (1), see [20].…”

Section: B Basis Matrices For the Dual Variable Zmentioning

confidence: 99%

“…SeDuMi [11] [19]. Preliminary results on the approach used in KYPD has been presented in [18] and [20] The KYP-SDP has the following structure …”

mentioning

confidence: 99%

“…They are based on cutting plane methods [13], [14], [15], [16], interior-point methods with an alternative barrier [14] and interior-point methods combined with conjugate gradients [17], [18], [19]. Preliminary results on the approach used in KYPD has been presented in [18] and [20] The KYP-SDP has the following structure…”

mentioning

confidence: 99%

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KYPD: a solver for semidefinite programs derived from the Kalman-Yakubovich-Popov lemma

Wallin

Hansson

2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508)

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Semidefinite programs derived from the Kalman-Yakubovich-Popov lemma are quite common in control and signal processing applications. The programs are often of high dimension making them hard or impossible to solve with general-purpose solvers. KYPD is a customized solver for KYP-SDPs that utilizes the inherent structure of the optimization problem thus improving efficiency significantly In applications the size of the SDP is often very large making it hard or even impossible to solve with generalpurpose software. However, the KYP-SDP has a very special structure that may be exploited to make efficient solvers. KYPD [9] is developed in YALMIP [10] and first utilizes the KYP-SDP structure to form an SDP with fewer variables. Then KYPD calls a general-purpose solver to actually solve the SDP. This solver can be any of YALMIPs interfaced primal-dual SDP-solvers, e.g. SeDuMi [11] [19]. Preliminary results on the approach used in KYPD has been presented in [18] and [20] The KYP-SDP has the following structure

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Section: Further Improvements Of the Solvermentioning

confidence: 89%

“…This implies that the operator F has full rank, [20]. To see this we first notice that P will not change if we apply feedback,Ã = A − BL.…”

Section: Assumptionsmentioning

confidence: 98%

Section: B Basis Matrices For the Dual Variable Zmentioning

confidence: 99%

“…SeDuMi [11] [19]. Preliminary results on the approach used in KYPD has been presented in [18] and [20] The KYP-SDP has the following structure …”

mentioning

confidence: 99%

mentioning

confidence: 99%

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KYPD: a solver for semidefinite programs derived from the Kalman-Yakubovich-Popov lemma

Wallin

Hansson

2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508)

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DREAMweb: An online tool for graph‐based modeling of NMR protein structure

Das,

Chaudhury,

Pal

2024

Proteomics

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The value of accurate protein structural models closely conforming to the experimental data is indisputable. DREAMweb deploys an improved DREAM algorithm, DREAMv2, that incorporates a tighter bound in the constraint set of the underlying optimization approach. This reduces the artifacts while modeling the protein structure by solving the distance‐geometry problem. DREAMv2 follows a bottom‐up strategy of building smaller substructures for regions with a larger concentration of experimental bounds and consolidating them before modeling the rest of the protein structure. This improves secondary structure conformance in the final models consistent with experimental data. The proposed method efficiently models regions with sparse coverage of experimental data by reducing the possibility of artifacts compared to DREAM. To balance performance and accuracy, smaller substructures ( atoms) are solved in this regime, allowing faster builds for the other parts under relaxed conditions. DREAMweb is accessible as an internet resource. The improvements in results are showcased through benchmarks on 10 structures. DREAMv2 can be used in tandem with any NMR‐based protein structure determination workflow, including an iterative framework where the NMR assignment for the NOESY spectra is incomplete or ambiguous. DREAMweb is freely available for public use at http://pallab.cds.iisc.ac.in/DREAM/ and downloadable at https://github.com/niladriranjandas/DREAMv2.git.

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IQC‐based robustness analysis of discrete‐time linear time‐varying systems

Fry

Farhood

Seiler

2017

Intl J Robust & Nonlinear

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Summary The paper investigates the robust stability and performance of uncertain linear time‐varying (LTV) systems using an integral quadratic constraint (IQC) based analysis approach. Specifically, previous theoretical work on IQC‐based robustness analysis of linear time‐invariant (LTI) systems is extended to discrete‐time LTV systems. In the case of a general LTV nominal system, the analysis solution is provided in terms of an infinite‐dimensional convex optimization problem. This optimization problem reduces into a finite‐dimensional semidefinite program when the nominal system in question is finite horizon, periodic, or, more generally, eventually periodic. Finally, the results are applied to an unmanned aircraft control system executing an aggressive maneuver, where the developed techniques are used to find the region in which the aircraft is guaranteed to reside at the end of its planned trajectory. Copyright © 2017 John Wiley & Sons, Ltd.

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Interior-Point Algorithms for Semidefinite Programming Problems Derived from the KYP Lemma

Cited by 69 publications

References 19 publications

KYPD: a solver for semidefinite programs derived from the Kalman-Yakubovich-Popov lemma

KYPD: a solver for semidefinite programs derived from the Kalman-Yakubovich-Popov lemma

DREAMweb: An online tool for graph‐based modeling of NMR protein structure

IQC‐based robustness analysis of discrete‐time linear time‐varying systems

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