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94
ANFIS: AdaptiveNetworkBased Fuzzy Inference System
, 1993
"... This paper presents the architecture and learning procedure underlying ANFIS (AdaptiveNetwork based Fuzzy Inference System), a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an inputoutput mapping bas ..."
Abstract

Cited by 432 (5 self)
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This paper presents the architecture and learning procedure underlying ANFIS (AdaptiveNetwork based Fuzzy Inference System), a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an inputoutput mapping based on both human knowledge (in the form of fuzzy ifthen rules) and stipulated inputoutput data pairs. In our simulation, we employ the ANFIS architecture to model nonlinear functions, identify nonlinear components onlinely in a control system, and predict a chaotic time series, all yielding remarkable results. Comparisons with artificail neural networks and earlier work on fuzzy modeling are listed and discussed. Other extensions of the proposed ANFIS and promising applications to automatic control and signal processing are also suggested. 1 Introduction System modeling based on conventional mathematical tools (e.g., differential equations) is not well suited for dealing with illdefine...
Illposed problems in early vision
 Proceedings of the IEEE
, 1988
"... The first processing stage in computational vision, also called early vision, consists of decoding twodimensional images in terms of properties of 30 surfaces. Early vision includes problems such as the recovery of motion and optical flow, shape from shading, surface interpolation, and edge detect ..."
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Cited by 178 (13 self)
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The first processing stage in computational vision, also called early vision, consists of decoding twodimensional images in terms of properties of 30 surfaces. Early vision includes problems such as the recovery of motion and optical flow, shape from shading, surface interpolation, and edge detection. These are inverse problems, which are often illposed or illconditioned. We review here the relevant mathematical results on illposed and illconditioned problems and introduce the formal aspects of regularization theory in the linear and nonlinear case. Specific topics in early vision and their regularization are then analyzed rigorously, characterizing existence, uniqueness, and stability of solutions.
Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
 J. Funct. Anal
, 1999
"... We study some problems on exponential integrability, concentration of measure, and transportation cost related to logarithmic Sobolev inequalities. On the real line, we then give a characterization of those probability measures which satisfy these inequalities 1999 Academic Press Key Words: logarith ..."
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Cited by 79 (4 self)
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We study some problems on exponential integrability, concentration of measure, and transportation cost related to logarithmic Sobolev inequalities. On the real line, we then give a characterization of those probability measures which satisfy these inequalities 1999 Academic Press Key Words: logarithmic Sobolev inequalities; exponential integrability; concentration of measure; transportation inequalities.
Method of invariant manifolds and regularization of acoustic spectra. Transport Theory and Stat
 Phys
, 1994
"... A new approach to the problem of reduced description for Boltzmanntype systems is developed. It involves a direct solution of two main problems: thermodynamici ty and dynamic invariance of reduced description. A universal construction is introduced, which gives a thermodynamic parameterization of a ..."
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Cited by 17 (11 self)
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A new approach to the problem of reduced description for Boltzmanntype systems is developed. It involves a direct solution of two main problems: thermodynamici ty and dynamic invariance of reduced description. A universal construction is introduced, which gives a thermodynamic parameterization of an almost arbitrary approximation. Newtontype procedures of successive approximations are developed which correct dynamic noninvariance. The method is applied to obtain corrections to the local Maxwell manifold uSlng parametrics expansions instead of Taylor series into powers of Knudsen number. In particular, the high frequency acoustic spectra is obtained. 1.
Numerical Solution of the Nonlinear PoissonBoltzmann Equation: Developing More Robust and Efficient Methods
 J. Comput. Chem
, 1995
"... this paper, we consider numerical solution of the nonlinear PoissonBoltzmann equation (PBE), the fundamental equation arising in the DebyeHuckel theory [1] of continuum molecular eletrostatics. In the case of a 1 : 1 electrolyte, this equation can be written as (#(r)#u(r)) + # (r) sinh(u(r) ..."
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Cited by 12 (5 self)
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this paper, we consider numerical solution of the nonlinear PoissonBoltzmann equation (PBE), the fundamental equation arising in the DebyeHuckel theory [1] of continuum molecular eletrostatics. In the case of a 1 : 1 electrolyte, this equation can be written as (#(r)#u(r)) + # (r) sinh(u(r)) = 4#e c kBT z i #(r r i ), u(#) = 0, (1) a threedimensional second order nonlinear partial differential equation governing the dimensionless electrostatic potential u(r) = e c #(r)/k 1 B T 1 , where #(r) is the electrostatic potential at a field position r. The importance of this equation for modeling biomolecules is wellestablished; more detailed discussions of the use of the PoissonBoltzmann equation may be found in the survey articles of Briggs and McCammon [2] and Sharp and Honig [3]
On Duality Theory of Conic Linear Problems
 in SemiInfinite Programming
, 2000
"... In this paper we discuss duality theory of optimization problems with a linear objective function and subject to linear constraints with cone inclusions, referred to as conic linear problems. We formulate the Lagrangian dual of a conic linear problem and survey some results based on the conjugate du ..."
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Cited by 12 (0 self)
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In this paper we discuss duality theory of optimization problems with a linear objective function and subject to linear constraints with cone inclusions, referred to as conic linear problems. We formulate the Lagrangian dual of a conic linear problem and survey some results based on the conjugate duality approach where the questions of "no duality gap" and existence of optimal solutions are related to properties of the corresponding optimal value function. We discuss in detail applications of the abstract duality theory to the problem of moments, linear semiinfinite and continuous linear programming problems. Key words: Conic linear programs, Lagrangian and conjugate duality, optimal value function, problem of moments, semiinfinite programming, continuous linear programming. AMS subject classification: 49N15, 90C34, 90C46 # Work performed at Argonne National Laboratory while a Faculty Research Participant. Program administered by the Argonne Division of Educational Programs with fun...
INEXACT JOSEPHY–NEWTON FRAMEWORK FOR GENERERALIZED EQUATIONS AND ITS APPLICATIONS TO LOCAL ANALYSIS OF NEWTONIAN METHODS FOR CONSTRAINED OPTIMIZATION ∗
, 2008
"... We propose and analyze a perturbed version of the classical JosephyNewton method for solving generalized equations. This perturbed framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilzed version, sequential quadratically constrained quadratic progr ..."
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Cited by 8 (6 self)
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We propose and analyze a perturbed version of the classical JosephyNewton method for solving generalized equations. This perturbed framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilzed version, sequential quadratically constrained quadratic programming, and linearly constrained Lagrangian methods. For the linearly constrained Lagrangian methods, in particular, we obtain superlinear convergence under the secondorder sufficient optimality condition and the strict Mangasarian–Fromovitz constraint qualification, while previous results in the literature assume (in addition to secondorder sufficiency) the stronger linear independence constraint qualification as well as the strict complementarity condition. For the sequential quadratically constrained quadratic programming methods, we prove primaldual superlinear/quadratic convergence under the same assumptions as above, which also gives a new result.
A Characterization of Lipschitzian Stability in Optimal Control
, 1998
"... . We consider a nonlinear optimal control problem with inequality control constraints and subject to canonical perturbations. We prove that the primaldual pair satisfying the firstorder necessary conditions is locally singlevalued and Lipschitz continuous, with the primal component being a locall ..."
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Cited by 8 (3 self)
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. We consider a nonlinear optimal control problem with inequality control constraints and subject to canonical perturbations. We prove that the primaldual pair satisfying the firstorder necessary conditions is locally singlevalued and Lipschitz continuous, with the primal component being a locally optimal solution, if and only if the combination of an independence conditions for the gradients of the active constraints and a coercivity condition holds. Key Words. Optimal Control, Canonical Perturbations, Lipschitzian Stability. AMS Classification. 49K40, 49K15. 1 Introduction In this paper we present necessary and su#cient conditions for lipschitzian stability in optimal control. We are motivated by the recently obtained characterization of the lipschitzian stability of the standard finitedimensional mathematical programming problem. Specifically, it was shown in [4] that the combination of the linear independence of the active constraints and the strong secondorder su#cient condi...
Duality and Existence for a Class of Mass Transportation Problems and Economic Applications
, 2000
"... We establish duality, existence and uniqueness results for a class of mass transportations problems. We extend a technique of W. Gangbo [9] using the Euler Equation of the dual problem. This is done by introducing the hFenchel Transform and using its basic properties. The cost functions we conside ..."
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Cited by 8 (2 self)
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We establish duality, existence and uniqueness results for a class of mass transportations problems. We extend a technique of W. Gangbo [9] using the Euler Equation of the dual problem. This is done by introducing the hFenchel Transform and using its basic properties. The cost functions we consider satisfy a generalization of the socalled SpenceMirrlees condition which is wellknown by economists in dimension 1. We therefore end this article by a somehow unexpected application to the economic theory of incentives. R'esum'e Nous 'etablissons dans cet article des r'esultats de dualit'e, d'existence et d'unicit 'e pour une classe de probl`emes de transport optimal de masse. La nouveaut 'e r'eside ici dans l'emploi de la transform'ee de Fenchel hconvexe qui permet d'utiliser un argument de W. Gangbo [9] consistant `a exploiter l"equation d'Euler du probl`eme dual. Les couts de transport que nous consid'erons satisfont une condition g'en'eralisant la condition de SpenceMirrlees bi...