nonlinear programming method
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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.

scholarly journals A NONLINEAR PROGRAMMING METHOD FOR DYNAMIC PROGRAMMING

2016 ◽  
Vol 21 (2) ◽  
pp. 336-361 ◽  
Author(s):  
Yongyang Cai ◽  
Kenneth L. Judd ◽  
Thomas S. Lontzek ◽  
Valentina Michelangeli ◽  
Che-Lin Su
Keyword(s):  
Dynamic Programming ◽  
Nonlinear Programming ◽  
Approximation Theory ◽  
Infinite Horizon ◽  
Numerical Results ◽  
Programming Method ◽  
Value Functions ◽  
Programming Formulation ◽  
Linear Approach ◽  
Nonlinear Programming Method

A nonlinear programming formulation is introduced to solve infinite-horizon dynamic programming problems. This extends the linear approach to dynamic programming by using ideas from approximation theory to approximate value functions. Our numerical results show that this nonlinear programming is efficient and accurate, and avoids inefficient discretization.

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