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A Global Optimization Method, αBB, for General TwiceDifferentiable Constrained NLPs: I  Theoretical Advances
, 1997
"... In this paper, the deterministic global optimization algorithm, αBB, (αbased Branch and Bound) is presented. This algorithm offers mathematical guarantees for convergence to a point arbitrarily close to the global minimum for the large class of twicedifferentiable NLPs. The key idea is the constru ..."
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Cited by 73 (4 self)
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In this paper, the deterministic global optimization algorithm, αBB, (αbased Branch and Bound) is presented. This algorithm offers mathematical guarantees for convergence to a point arbitrarily close to the global minimum for the large class of twicedifferentiable NLPs. The key idea is the construction of a converging sequence of upper and lower bounds on the global minimum through the convex relaxation of the original problem. This relaxation is obtained by (i) replacing all nonconvex terms of special structure (i.e., bilinear, trilinear, fractional, fractional trilinear, univariate concave) with customized tight convex lower bounding functions and (ii) by utilizing some α parameters as defined by Maranas and Floudas (1994b) to generate valid convex underestimators for nonconvex terms of generic structure. In most cases, the calculation of appropriate values for the α parameters is a challenging task. A number of approaches are proposed, which rigorously generate a set of α par...
An algorithm for the real interval eigenvalue problem. Research Report RR6680
, 2008
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 9 (8 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. appor t de r ech er ch e
Bounds on real eigenvalues and singular values of interval matrices
 SIAM J. Matrix Anal. Appl
"... Abstract. We study bounds on real eigenvalues of interval matrices, and our aim is to develop fast computable formulae that produce assharpaspossible bounds. We consider two cases: general and symmetric interval matrices. We focus on the latter case, since on the one hand such interval matrices h ..."
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Cited by 7 (0 self)
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Abstract. We study bounds on real eigenvalues of interval matrices, and our aim is to develop fast computable formulae that produce assharpaspossible bounds. We consider two cases: general and symmetric interval matrices. We focus on the latter case, since on the one hand such interval matrices have many applications in mechanics and engineering, and on the other hand many results from classical matrix analysis could be applied to them. We also provide bounds for the singular values of (generally nonsquare) interval matrices. Finally, we illustrate and compare the various approaches by a series of examples.
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"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit:
Robust State Feedback for Interval Systems: An Interval Analysis Approach ∗
"... The problem of robust state feedback design for a linear dynamical system with uncertain (interval) parameters is considered. The designed state feedback controller has to place all the coefficients of the closed loop system characteristic polynomial within assigned closed loop interval characterist ..."
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The problem of robust state feedback design for a linear dynamical system with uncertain (interval) parameters is considered. The designed state feedback controller has to place all the coefficients of the closed loop system characteristic polynomial within assigned closed loop interval characteristic polynomial. A condition is derived using certain known facts about matrix minors and its characteristic equation. The derived condition assigns the closed loop coefficients of the system characteristic polynomial within the assigned closed loop interval polynomial, if certain inequalities admit a positive solution. The method is simple and has advantage that it does not require system canonical transformation. The efficacy of the method is illustrated using numerical examples.
IN
, 2009
"... problem. [Research Report] RR7057, 2009, pp.14. <inria00422966> ..."
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Robust stability check of fractional order linear time invariant systems with interval uncertainties
, 2005
"... For uncertain fractionalorder linear time invariant (FOLTI) systems with interval coefficients described in state space form, the robust stability check problem is solved for the first time in this paper. Both the checking procedure and the Matlab code are presented with two illustrative examples. ..."
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For uncertain fractionalorder linear time invariant (FOLTI) systems with interval coefficients described in state space form, the robust stability check problem is solved for the first time in this paper. Both the checking procedure and the Matlab code are presented with two illustrative examples. The conservatism is shown to be small. r 2006 Elsevier B.V. All rights reserved.