Loss Models For Broadband Networks With Non-Linear Constraint Functions

1999 ◽  
pp. 121-134 ◽  
Author(s):  
William Liang ◽  
Keith W. Ross
Keyword(s):  
Linear Constraint ◽  
Broadband Networks ◽  
Non Linear ◽  
Loss Models

Multiple Optimal Solutions in the Portfolio Selection Model with Short-Selling

2003 ◽  
Vol 06 (07) ◽  
pp. 703-720
Author(s):  
A. Schianchi ◽  
L. Bongini ◽  
M. D. Esposti ◽  
C. Giardinà
Keyword(s):  
Portfolio Optimization ◽  
Optimal Solution ◽  
Real Data ◽  
Linear Constraint ◽  
Short Selling ◽  
Nonlinear Constraint ◽  
Risk Levels ◽  
Margin Requirements ◽  
Non Linear ◽  
Portfolio Optimization Problem

In this paper an extension of the Lintner model [1] is considered: the problem of portfolio optimization is studied when short-selling is allowed through the mechanism of margin requirements. This induces a non-linear constraint on the wealth. When interest on deposited margin is present, Lintner ingeniously solved the problem by recovering the unique optimal solution of the linear model (no margin requirements). In this paper an alternative and more realistic approach is explored: the nonlinear constraint is maintained but no interest is perceived on the money deposited against short-selling. This leads to a fully non-linear problem which admits multiple and unstable solutions very different among themselves but corresponding to similar risk levels. Our analysis is built on a seminal idea by Galluccio, Bouchaud and Potters [3], who have re-stated the problem of finding solutions of the portfolio optimization problem in futures markets in terms of a spin glass problem. In order to get the best portfolio (i.e. the one lying on the efficiency frontier), we have to implement a two-step procedure. A worked example with real data is presented.

Non-Linear Constraints and Stiffness Representations in Simple Flexible-Body Dynamic Beam Formulations

2003 ◽  
Vol 9 (8) ◽  
pp. 911-929 ◽  
Author(s):  
William Haering
Keyword(s):  
Linear Constraint ◽  
Linear Constraints ◽  
Model Verification ◽  
Lumped Parameter Model ◽  
Flexible Body ◽  
Flexible Beam ◽  
Lumped Parameter ◽  
Non Linear ◽  
Linear Spring ◽  
Insight Into

Abstract: A simple discrete four-degree-of-freedom (lumped parameter) model representing a flexible beam undergoing large overall planar prescribed motion has been developed. It serves as a simple tool to investigate two previously studied problems involving flexible-body beam dynamics, namely those involving bending and membrane stiffness dominated behavior. The tool is used to investigate the requirements to accurately solve these problems using non-linear constraints and a non-linear spring representation. The validity of this model is demonstrated by comparing results to those previously published for continuous flexible-body beam formulations. One of these continuous representations is modified to include a non-linear tether spring representation. This allows additional model verification as well as insight into the non-linear constraint and stiffness representations. Taken in its entirety, this investigation demonstrates the utility of these simple lumped parameter models, by showing their ability to provide rapid insight into the behavior of the more complicated continuous models, as well as the system in general.

Large Amplitude Free Vibration Analysis of a Rotating Beam with Non-linear Spring and Mass System

2005 ◽  
Vol 11 (12) ◽  
pp. 1511-1533 ◽  
Author(s):  
S. K. Das ◽  
P. C. Ray ◽  
G. Pohit
Keyword(s):  
Free Vibration Analysis ◽  
Linear Constraint ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Rotating Beam ◽  
Mass System ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
Out Of Plane ◽  
Linear Spring

The free, out-of-plane vibration of a rotating beam with a non-linear spring-mass system has been investigated. The non-linear constraint appears in the boundary condition. The solution is obtained by applying the method of multiple time-scales directly to the non-linear partial differential equations and the boundary conditions. The results of the linear frequencies match well with those obtained in the literature. Subsequent non-linear study indicates that there is a pronounced effect of the spring and its mass. The influence of the spring-mass location on frequencies is also investigated for the non-linear frequencies of the rotating beam.

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