Easier than We Thought - A Practical Scheme to Compute Pessimistic Bilevel Optimization Problem

2015 ◽  
Author(s):  
Bo Zeng
Keyword(s):  
Optimization Problem ◽  
Bilevel Optimization ◽  
Practical Scheme

Optimality results for a specific bilevel optimization problem

Optimization ◽  
2011 ◽  
Vol 60 (7) ◽  
pp. 813-822 ◽  
Author(s):  
S. Dempe ◽  
N. Gadhi
Keyword(s):  
Optimization Problem ◽  
Bilevel Optimization

Anticipatory Optimization of Traffic Control

2000 ◽  
Vol 1725 (1) ◽  
pp. 109-115 ◽  
Author(s):  
Henk J. van Zuylen ◽  
Henk Taale
Keyword(s):  
Traffic Control ◽  
Optimization Problem ◽  
Bilevel Optimization ◽  
Simulation Studies ◽  
Traffic Flows ◽  
System Optimum ◽  
Time Model ◽  
Traffic Conditions ◽  
Made In ◽  
Small Disturbances

Traffic control and travelers’ behavior are two mutually influential processes with different objectives. Decisions made in traffic control influence travelers’ possibilities in choosing their preferred mode, route, and time of departure; and the choices made by travelers influence the optimization possibilities for traffic control. This research presents the results of simulation studies and a mathematical analysis of this bilevel optimization problem. Under certain conditions, multiple stable situations are possible, but some of these situations are sensitive to small disturbances by which the system moves away from the original equilibrium state. There appears to be a nonlinear relationship between system parameters and the character and location of the equilibrium situations. The details of the travel time model appear to have a large influence. If road authorities want to optimize traffic control, they have to anticipate the reaction of travelers. This makes the optimization process much more complicated. Iterative optimization, where traffic control is adjusted as soon as traffic conditions change, generally does not lead to a system optimum. Methods are therefore necessary that allow for the optimization of traffic control while taking into account that traffic flows will change as a result of traffic control.

scholarly journals A Fixed-Point Subgradient Splitting Method for Solving Constrained Convex Optimization Problems

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 377
Author(s):  
Nimit Nimana
Keyword(s):  
Fixed Point ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Splitting Method ◽  
Optimal Solution ◽  
Bilevel Optimization ◽  
Convergence Properties ◽  
Nonlinear Operators ◽  
Convex Optimization Problems ◽  
Feasible Points

In this work, we consider a bilevel optimization problem consisting of the minimizing sum of two convex functions in which one of them is a composition of a convex function and a nonzero linear transformation subject to the set of all feasible points represented in the form of common fixed-point sets of nonlinear operators. To find an optimal solution to the problem, we present a fixed-point subgradient splitting method and analyze convergence properties of the proposed method provided that some additional assumptions are imposed. We investigate the solving of some well known problems by using the proposed method. Finally, we present some numerical experiments for showing the effectiveness of the obtained theoretical result.

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