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(1) THE CLUSTER PROBLEM IN GLOBAL OPTIMIZATION THE
"... �������� � We consider a branch and bound method for enclosing all global minimizers of a nonlinear C 2 or C 1 objective function. In particular, we consider bounds obtained with interval arithmetic, along with the “midpoint test, ” but no acceleration procedures. Unless the lower bound is exact, th ..."
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near the global minimizers and to the order of the corresponding interval extension. Das Cluster Problem bei globalen Optimierungsaufgaben Wir betrachten ein Bisektionsverfahren zur Einschließung aller globalen Minimalpunkte für stetig differenzierbare bzw. zweimal stetig differenzierbare
Interior Point Methods for Mathematical Programming: a Bibliography, Diskussionsbeitrag Nr
, 1991
"... Nothing is older than a yesterday’s newspaper! In this sense, this bibliography is incomplete, of course, because of the enormous interest and ongoing research in interior–point methods for mathematical programming. These activities were initiated by Karmarkar’s polynomial–time linear programming al ..."
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Cited by 11 (0 self)
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Nothing is older than a yesterday’s newspaper! In this sense, this bibliography is incomplete, of course, because of the enormous interest and ongoing research in interior–point methods for mathematical programming. These activities were initiated by Karmarkar’s polynomial–time linear programming algorithm in 1984, resulting in a flood of research papers, articles, talks, developments of commercial software and so on. This working paper should be regarded as a first trial to obtain a survey over the research reports, journal articles, etc., published so far, resp. known to the author. Acknowledgements:
A Quadratic Programming Bibliography
, 2001
"... A method for restoring an optical image which is subjected to lowpass frequency filtering is presented. It is assumed that the object whose image is restored is of finite spatial extent. The problem is treated as an algebraic imagerestoration problem which is then solved as a quadratic programming ..."
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Cited by 8 (0 self)
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A method for restoring an optical image which is subjected to lowpass frequency filtering is presented. It is assumed that the object whose image is restored is of finite spatial extent. The problem is treated as an algebraic imagerestoration problem which is then solved as a quadratic programming problem with bounded variables. The regularization technique for the illposed system is to replace the consistent system of the quadratic programming problem by an approximate system of smaller rank. The rank which gives a best or nearbest solution is estimated. This method is a novel one, and it compares favorably with other known methods. Computersimulated examples are presented. Comments and conclusions are given.
The Cluster Problem in Global Optimization  The Univariate Case
, 1993
"... We consider a branch and bound method for enclosing all global minimizers of a nonlinear C² or C¹ objective function. In particular, we consider bounds obtained with interval arithmetic, along with the "midpoint test," but no acceleration procedures. Unless the lower bound is exact, the al ..."
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Cited by 4 (3 self)
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We consider a branch and bound method for enclosing all global minimizers of a nonlinear C² or C¹ objective function. In particular, we consider bounds obtained with interval arithmetic, along with the "midpoint test," but no acceleration procedures. Unless the lower bound is exact, the algorithm without acceleration procedures in general gives an undesirable cluster of intervals around each minimizer. In this article, we analyze this problem in the one dimensional case. Theoretical results are given which show that the problem is highly related to the behavior of the objective function near the global minimizers and to the order of the corresponding interval extension.
Algorithms for the Constrained Design of Digital Filters with Arbitrary Magnitude and Phase Responses
, 1999
"... This thesis presents several new algorithms for designing digital filters subject to specifications in the frequency domain. Finite impulse response (FIR) as well as infinite impulse response (IIR) filter design problems are considered. Unlike many ..."
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Cited by 6 (0 self)
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This thesis presents several new algorithms for designing digital filters subject to specifications in the frequency domain. Finite impulse response (FIR) as well as infinite impulse response (IIR) filter design problems are considered. Unlike many
The Application of Shooting to Singular Boundary Value Problems
, 1999
"... This project was supported by the ..."
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"... am Werkzeugmaschinenlabor (WZL) der RheinischWestfälischen Technischen Hochschule ..."
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am Werkzeugmaschinenlabor (WZL) der RheinischWestfälischen Technischen Hochschule
Theory
, 1997
"... Method of a small parameter for a class of nonautonomous systems of second order differential equations with impulses Integral inequalities for piecewice – continuous functions of many variables ..."
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Method of a small parameter for a class of nonautonomous systems of second order differential equations with impulses Integral inequalities for piecewice – continuous functions of many variables
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