Journal ArticleDOI
A Variational Approach to Lagrange Multipliers
Jonathan M. Borwein,Qiji J. Zhu +1 more
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Lagrange multiplier rules from a variational perspective is discussed, to highlight many of the issues involved and also to illustrate how broadly an abstract version can be applied.Abstract:
We discuss Lagrange multiplier rules from a variational perspective. This allows us to highlight many of the issues involved and also to illustrate how broadly an abstract version can be applied.read more
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A General Framework for Portfolio Theory : Part I: theory and various models
TL;DR: In this paper, the authors show that the trade-off between utility and risk for investment portfolios happens on a convex curve in the two-dimensional space of utility and risks.
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An Overview of Numerical Methods for Incompressible Viscous Flow with Moving Particles
Yuching Wu,Bin Yang +1 more
TL;DR: An overview of the representative methods for the simulation of incompressible viscous flow with moving boundaries based on conforming or nonconforming meshes, including the distributed Lagrange multiplier/fictitious domain method, the immersed boundary method, and the arbitrary Lagrange–Eulerian method are presented.
Journal ArticleDOI
Sustainability analysis of reused industrial buildings in China: an assessment method
Abstract: The sustainable development of old industrial buildings is in line with the national construction strategy and has an important impact on current urban renewal. Only by achieving a unified balance among economic, social, and environmental factors can reused industrial buildings be considered sustainable. However, there are no relevant sustainability assessment indicators and methods for reused industrial buildings in China. The purpose of this study was to provide a reasonable and effective method for assessing the sustainability of reused industrial buildings. First, this study analysed the factors influencing reused industrial building sustainability through a project investigation. Second, based on the assessment indicator setting procedure, the sustainability assessment indicator system for reused industrial buildings was optimised. Moreover, a multi-level sustainability assessment model based on extenics was established to identify the correlation functions of indicators with different attributes. Finally, a case was considered to verify this assessment method. The results showed that this assessment method in good agreement with the actual state of the case was validated to be more effective and practical. The assessment method could provide a basis for decision-making to improve sustainability and could be adopted by relevant rating agencies to determine the sustainability level of reused industrial buildings.
Effective Field Theory of Particle Interactions Mediated by Fluid Surfaces
TL;DR: The Effective Field Theory (EFT) formalism as discussed by the authors disentangles the particle boundary conditions from the calculation of the interaction free energy by constructing an equivalent point-particle description.
References
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Book
Optimization and nonsmooth analysis
TL;DR: The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.
Book
Optimization by Vector Space Methods
TL;DR: This book shows engineers how to use optimization theory to solve complex problems with a minimum of mathematics and unifies the large field of optimization with a few geometric principles.
Book
Variational Analysis and Generalized Differentiation II
TL;DR: In this article, the authors propose a constrained optimization and equilibrium approach for optimal control of evolution systems in Banach spaces. And they apply this approach to distributed systems in economics applications.