On generalized semi-infinite programming

“…In [90,[97][98][99]101], we connected the discrete mathematics of networks with GSIP, by this introducing a new and pioneering scientific approach into computational biology. GSIP is an advancing wide problem class with many motivations, results, future challenges, and many practical applications even today [76,78,96].…”

Section: Introductionmentioning

confidence: 99%

“…GSIP revisited and applied for our gene-environment network problem (4), reveals the following general program form [76,78,96]:…”

Section: Introductionmentioning

confidence: 99%

A New Mathematical Approach in Environmental and Life Sciences: Gene–Environment Networks and Their Dynamics

Weber¹,

Gök

Söyler

2008

Environ Model Assess

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An important research area in life sciences is devoted to modeling, prediction, and dynamics of geneexpression patterns. As clearly understood in these days, this enterprise cannot become satisfactory without acknowledging the role of the environment. To a representation of past, present, and most likely future states, we also encounter measurement errors and uncertainties. This paper surveys and improves recent advances in understanding the foundations and interdisciplinary implications of the newly introduced geneenvironment networks, and it integrates the important theme of carbon dioxide emission reduction into the networks and dynamics. We also introduce some operational and managerial issues of practical working and decision making, expressed in terms of sliding windows, quadrants (modules) of parametric effects, and navigating (controlling) between such effects and directing them. Given data from DNA microarray experiments and environmental records, we extract nonlinear ordinary differential equations that contain parameters that have to be determined. For this, we employ modern (Chebychevian) approximation and (generalized semi-infinite) optimization. After this is provided, timediscretized dynamical systems are studied. A combinatorial algorithm with polyhedra sequences allows to detect the region of parametric stability. Finally, we analyze the topological landscape of gene-environment networks with its structural (in)stability. By embedding as a module and investigating CO 2 emission control and figuring out game theoretical aspects, we conclude. This pioneering work is theoretically elaborated, practically devoted to health care, medicine, education, living conditions, and environmental protection, and it invites the readers to future research.

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“…Finally, the set of definition of the constraint functional is deformed with the design domain. In the related context of generalized semi-infinite programming, solution methods have been developed only when the number of decision variables is finite and the problem has a special structure [28,29,34].…”

Section: Introductionmentioning

confidence: 99%

A penalty method for topology optimization subject to a pointwise state constraint

Amstutz¹

2009

ESAIM: COCV

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Abstract. This paper deals with topology optimization of domains subject to a pointwise constraint on the gradient of the state. To realize this constraint, a class of penalty functionals is introduced and the expression of the corresponding topological derivative is obtained for the Laplace equation in two space dimensions. An algorithm based on these concepts is proposed. It is illustrated by some numerical applications.Mathematics Subject Classification. 49Q10, 49Q12, 49M30, 35J05.

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On generalized semi-infinite programming

Cited by 11 publications

References 53 publications

On generalized semi-infinite optimization of genetic networks

On generalized semi-infinite optimization of genetic networks

A New Mathematical Approach in Environmental and Life Sciences: Gene–Environment Networks and Their Dynamics

A penalty method for topology optimization subject to a pointwise state constraint

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