Upper bound shakedown analysis of foundations on cohesive-frictional soil based on a nonlinear programming method

2021 ◽  
Vol 130 ◽  
pp. 103904
Author(s):  
Mohammad Mojallal ◽  
Orang Farzaneh ◽  
Faradjollah Askari
Keyword(s):  
Nonlinear Programming ◽  
Upper Bound ◽  
Programming Method ◽  
Shakedown Analysis ◽  
Nonlinear Programming Method

scholarly journals Efficiency Loss of Mixed Equilibrium Behaviors with Polynomial Cost Functions

2012 ◽  
Vol 22 (5) ◽  
pp. 325-331 ◽  
Author(s):  
Xiaojun Yu ◽  
Hai-Jun Huang
Keyword(s):  
Nonlinear Programming ◽  
Upper Bound ◽  
User Equilibrium ◽  
Programming Method ◽  
Cost Functions ◽  
Selfish Routing ◽  
Scaling Method ◽  
Efficiency Loss ◽  
Mixed Equilibrium ◽  
Nonlinear Programming Method

This paper investigates the efficiency loss of selfish routing simultaneously with user equilibrium (UE) player and Cournot-Nash (CN) players. The upper bound of the efficiency loss of UE-CN mixed equilibrium with polynomial cost functions is obtained by the scaling method and the nonlinear programming method, respectively. It is shown that the upper bound of efficiency loss obtained by the scaling method only depends on the polynomial degree of the link travel cost function and the upper bound of efficiency loss obtained by the nonlinear programming method depends on the number of the CN players besides the aforementioned factors. The numerical tests validate our analytical results. KEY WORDS: efficiency loss, UE-CN mixed equilibrium, variational inequality, selfish routing game

Optimal Fair Division for Measures with Piecewise Linear Density Functions

2017 ◽  
Vol 19 (02) ◽  
pp. 1750009 ◽  
Author(s):  
Jerzy Legut
Keyword(s):  
Nonlinear Programming ◽  
Linear Density ◽  
Piecewise Linear ◽  
Fair Division ◽  
Unit Interval ◽  
Programming Method ◽  
Probability Measures ◽  
Density Functions ◽  
Nonlinear Programming Method

A nonlinear programming method is used for finding an optimal fair division of the unit interval [Formula: see text] among [Formula: see text] players. Preferences of players are described by nonatomic probability measures [Formula: see text] with piecewise linear (PWL) density functions. The presented algorithm can be applied for obtaining “almost” optimal fair divisions for measures with arbitrary density functions approximable by PWL functions. The number of cuts needed for obtaining such divisions is given.

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