A Nonlinear Programming Method with Arbitrary Restrictions

2016 ◽  
Vol 2 (81) ◽  
pp. 2-10 ◽  
Author(s):  
A. Yu. Kuchmin ◽  
Keyword(s):  
Nonlinear Programming ◽  
Programming Method ◽  
Nonlinear Programming Method

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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