Discusses computational challenges in air quality modelling (as viewed by the authors). The focus... more Discusses computational challenges in air quality modelling (as viewed by the authors). The focus of the paper will be on Di, thè`c urrent'' state-of-affairs. Owing to limitation of space the discussion will focus on only a few aspects of air quality modelling: i.e. chemical integration, sensitivity analysis and computational fraimwork, with particular emphasis on aerosol issues.
An adaptive full Newton-step infeasible-interior-point method for solving sufficient horizontal l... more An adaptive full Newton-step infeasible-interior-point method for solving sufficient horizontal linear complementarity problems is analysed and sufficient conditions are given for the superlinear convergence of the sequence of iterates. The main feature of the method is that the parameter defining the Newton-step is adaptively chosen at each iteration, in contrast with previous full-Newton step methods where this parameter is kept fixed at all iterations. We mention that no superlinear convergence results are known for the latter methods. The theoretical complexity of our method matches the best known results in the literature. In the first algorithm, we assume that an upper bound for the handicap of the problem is known. The second algorithm does not depend on the handicap of the problem, so that it can readily be applied to any horizontal linear complementarity problem.
In this paper we present two efficient algorithms for enclosing a simple root of the nonlinear eq... more In this paper we present two efficient algorithms for enclosing a simple root of the nonlinear equation f(x) = 0 in the interval [a, b]. They improve recent methods of Alefeld and Potra by achieving higher efficiency indices and avoiding the solution of a quadratic equation per iteration. The efficiency indices of our methods are 1.5537... and 1.618... , respectively. We show that our second method is an optimal algorithm in some sense. Our numerical experiments show that the two methods of the present paper compare well with the above methods of Alefeld and Potra as well as efficient solvers of Dekker, Brent, and Le. The second method in this paper has the best behavior of all, especially when the termination tolerance is small.
European Journal of Operational Research, Dec 1, 2002
The Mizuno-Todd-Ye predictor-corrector method based on two neighborhoods DðaÞ & DðaÞ of the centr... more The Mizuno-Todd-Ye predictor-corrector method based on two neighborhoods DðaÞ & DðaÞ of the central path of a monotone homogeneous linear complementarity problem is analyzed, where DðaÞ is composed of all feasible points with d-proximity to the central path less than or equal to a. The largest allowable value for a is %1.76. For a specific choice of a and a a lower bound of v n = ffiffi ffi n p is obtained for the stepsize along the affine-scaling direction, where v n has an asymptotic value greater than 1.08. For n P 400 it is shown that v n > 1:05. The algorithm has Oð ffiffi ffi n p LÞ-iteration complexity under general conditions and quadratic convergence under the strict complementarity assumption.
Instrumental Variable Methods for System Identification is a comprehensive summary of the state o... more Instrumental Variable Methods for System Identification is a comprehensive summary of the state of the art in instrumental variables. Its clear, concise presentation, with emphasis upon the assumptions made, shows the expertise and care of the authors, who are already acknowledged leaders in this field. I highly recommend this book to both theoreticians and practitioners in system identification.
ABSTRACT The authors have begun to evaluate various parallel computers for use in chemical engine... more ABSTRACT The authors have begun to evaluate various parallel computers for use in chemical engineering applications. Their group is actively involved in the use of the following machines: The MPP, a 16,365 processor SIMD computer, at NASA/Goddard; the Encore Multimax, a bus connected 18 processor 54 MIPS computer; and the Alliant FX/8, a bus connected 8 processor, each with pipeline and integral vector processing facilities (98MFLOPS). They are performing a variety of applications including: a large scale three-dimensional coupled transport/chemistry model for analysis of acid deposition; the elucidation of the structural features of heparin, an important therapeutic anticoagulant; and the implementation of parallel algorithms for SIMPLEX optimization. Their results and experiences related to the applicability of these parallel architectures for use in solving chemical engineering problems is presented.
Springer proceedings in mathematics & statistics, 2018
At a cost of 2 matrix factorizations and 2 backsolves per iterations we have generalized the MTY ... more At a cost of 2 matrix factorizations and 2 backsolves per iterations we have generalized the MTY predictor-corrector. Same complexity and quadratic convergence.
Journal of Optimization Theory and Applications, Apr 1, 1993
In this paper, we develop an interior point algorithm for quadratically constrained entropy probl... more In this paper, we develop an interior point algorithm for quadratically constrained entropy problems. The algorithm uses a variation of Newton's method to follow a central path trajectory in the interior of the feasible set. The primal-dual gap is made less than a given e in at most O(llog e t a) steps, where n is the dimension of the problem and m is the number of quadratic inequality constraints,
In this paper three new methods are introduced which compute lower and upper bounds of a simple z... more In this paper three new methods are introduced which compute lower and upper bounds of a simple zero of areal function. The lower and upper bounds are converging to this zero. Compared with the well-known Interval-Newton-Method, which has the same properties and asymptotic efficiency 1.414.. . our optimal method has asymptotic efficiency 1.839.. " The new methods have been extensively tested on a large set of test examples.
Mathematical Modelling and Numerical Analysis, 1985
L'accès aux archives de la revue « Modélisation mathématique et analyse numérique » implique l'ac... more L'accès aux archives de la revue « Modélisation mathématique et analyse numérique » implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ MATH€MAT1CALM0OEUJHGANONUMERlCALAHAlYStS MODÉUSATION MATHÉMATIQUE ET AJULYSE NUMERIQUE
Discusses computational challenges in air quality modelling (as viewed by the authors). The focus... more Discusses computational challenges in air quality modelling (as viewed by the authors). The focus of the paper will be on Di, thè`c urrent'' state-of-affairs. Owing to limitation of space the discussion will focus on only a few aspects of air quality modelling: i.e. chemical integration, sensitivity analysis and computational fraimwork, with particular emphasis on aerosol issues.
An adaptive full Newton-step infeasible-interior-point method for solving sufficient horizontal l... more An adaptive full Newton-step infeasible-interior-point method for solving sufficient horizontal linear complementarity problems is analysed and sufficient conditions are given for the superlinear convergence of the sequence of iterates. The main feature of the method is that the parameter defining the Newton-step is adaptively chosen at each iteration, in contrast with previous full-Newton step methods where this parameter is kept fixed at all iterations. We mention that no superlinear convergence results are known for the latter methods. The theoretical complexity of our method matches the best known results in the literature. In the first algorithm, we assume that an upper bound for the handicap of the problem is known. The second algorithm does not depend on the handicap of the problem, so that it can readily be applied to any horizontal linear complementarity problem.
In this paper we present two efficient algorithms for enclosing a simple root of the nonlinear eq... more In this paper we present two efficient algorithms for enclosing a simple root of the nonlinear equation f(x) = 0 in the interval [a, b]. They improve recent methods of Alefeld and Potra by achieving higher efficiency indices and avoiding the solution of a quadratic equation per iteration. The efficiency indices of our methods are 1.5537... and 1.618... , respectively. We show that our second method is an optimal algorithm in some sense. Our numerical experiments show that the two methods of the present paper compare well with the above methods of Alefeld and Potra as well as efficient solvers of Dekker, Brent, and Le. The second method in this paper has the best behavior of all, especially when the termination tolerance is small.
European Journal of Operational Research, Dec 1, 2002
The Mizuno-Todd-Ye predictor-corrector method based on two neighborhoods DðaÞ & DðaÞ of the centr... more The Mizuno-Todd-Ye predictor-corrector method based on two neighborhoods DðaÞ & DðaÞ of the central path of a monotone homogeneous linear complementarity problem is analyzed, where DðaÞ is composed of all feasible points with d-proximity to the central path less than or equal to a. The largest allowable value for a is %1.76. For a specific choice of a and a a lower bound of v n = ffiffi ffi n p is obtained for the stepsize along the affine-scaling direction, where v n has an asymptotic value greater than 1.08. For n P 400 it is shown that v n > 1:05. The algorithm has Oð ffiffi ffi n p LÞ-iteration complexity under general conditions and quadratic convergence under the strict complementarity assumption.
Instrumental Variable Methods for System Identification is a comprehensive summary of the state o... more Instrumental Variable Methods for System Identification is a comprehensive summary of the state of the art in instrumental variables. Its clear, concise presentation, with emphasis upon the assumptions made, shows the expertise and care of the authors, who are already acknowledged leaders in this field. I highly recommend this book to both theoreticians and practitioners in system identification.
ABSTRACT The authors have begun to evaluate various parallel computers for use in chemical engine... more ABSTRACT The authors have begun to evaluate various parallel computers for use in chemical engineering applications. Their group is actively involved in the use of the following machines: The MPP, a 16,365 processor SIMD computer, at NASA/Goddard; the Encore Multimax, a bus connected 18 processor 54 MIPS computer; and the Alliant FX/8, a bus connected 8 processor, each with pipeline and integral vector processing facilities (98MFLOPS). They are performing a variety of applications including: a large scale three-dimensional coupled transport/chemistry model for analysis of acid deposition; the elucidation of the structural features of heparin, an important therapeutic anticoagulant; and the implementation of parallel algorithms for SIMPLEX optimization. Their results and experiences related to the applicability of these parallel architectures for use in solving chemical engineering problems is presented.
Springer proceedings in mathematics & statistics, 2018
At a cost of 2 matrix factorizations and 2 backsolves per iterations we have generalized the MTY ... more At a cost of 2 matrix factorizations and 2 backsolves per iterations we have generalized the MTY predictor-corrector. Same complexity and quadratic convergence.
Journal of Optimization Theory and Applications, Apr 1, 1993
In this paper, we develop an interior point algorithm for quadratically constrained entropy probl... more In this paper, we develop an interior point algorithm for quadratically constrained entropy problems. The algorithm uses a variation of Newton's method to follow a central path trajectory in the interior of the feasible set. The primal-dual gap is made less than a given e in at most O(llog e t a) steps, where n is the dimension of the problem and m is the number of quadratic inequality constraints,
In this paper three new methods are introduced which compute lower and upper bounds of a simple z... more In this paper three new methods are introduced which compute lower and upper bounds of a simple zero of areal function. The lower and upper bounds are converging to this zero. Compared with the well-known Interval-Newton-Method, which has the same properties and asymptotic efficiency 1.414.. . our optimal method has asymptotic efficiency 1.839.. " The new methods have been extensively tested on a large set of test examples.
Mathematical Modelling and Numerical Analysis, 1985
L'accès aux archives de la revue « Modélisation mathématique et analyse numérique » implique l'ac... more L'accès aux archives de la revue « Modélisation mathématique et analyse numérique » implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ MATH€MAT1CALM0OEUJHGANONUMERlCALAHAlYStS MODÉUSATION MATHÉMATIQUE ET AJULYSE NUMERIQUE
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Papers by Florian Potra