A self-adaptive gradient projection algorithm for the nonadditive traffic equilibrium problem

2012 ◽  
Vol 39 (2) ◽  
pp. 127-138 ◽  
Author(s):  
Anthony Chen ◽  
Zhong Zhou ◽  
Xiangdong Xu
Keyword(s):  
Equilibrium Problem ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Traffic Equilibrium ◽  
Gradient Projection Algorithm ◽  
Traffic Equilibrium Problem ◽  
Self Adaptive

scholarly journals Relaxed gradient projection algorithm for constrained node-based shape optimization

2021 ◽  
Author(s):  
Ihar Antonau ◽  
Majid Hojjat ◽  
Kai-Uwe Bletzinger
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Design Parameters ◽  
Active Set ◽  
Physical Constraints ◽  
Original Algorithm ◽  
Gradient Projection Algorithm ◽  
Non Linear

AbstractIn node-based shape optimization, there are a vast amount of design parameters, and the objectives, as well as the physical constraints, are non-linear in state and design. Robust optimization algorithms are required. The methods of feasible directions are widely used in practical optimization problems and know to be quite robust. A subclass of these methods is the gradient projection method. It is an active-set method, it can be used with equality and non-equality constraints, and it has gained significant popularity for its intuitive implementation. One significant issue around efficiency is that the algorithm may suffer from zigzagging behavior while it follows non-linear design boundaries. In this work, we propose a modification to Rosen’s gradient projection algorithm. It includes the efficient techniques to damp the zigzagging behavior of the original algorithm while following the non-linear design boundaries, thus improving the performance of the method.

scholarly journals Improved Gradient Projection Algorithm for Deblurred Image Application

2020 ◽  
Vol 1575 ◽  
pp. 012021
Author(s):  
Haixia Yan ◽  
Yanjun Liu
Keyword(s):  
Gradient Projection ◽  
Projection Algorithm ◽  
Gradient Projection Algorithm

Are We Really Solving the Dynamic Traffic Equilibrium Problem with a Departure Time Choice?

2018 ◽  
Vol 52 (3) ◽  
pp. 603-620 ◽  
Author(s):  
Ren-Yong Guo ◽  
Hai Yang ◽  
Hai-Jun Huang
Keyword(s):  
Equilibrium Problem ◽  
Traffic Equilibrium ◽  
Dynamic Traffic ◽  
Departure Time ◽  
Departure Time Choice ◽  
Traffic Equilibrium Problem

scholarly journals A Regularized Gradient Projection Method for the Minimization Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Yonghong Yao ◽  
Shin Min Kang ◽  
Wu Jigang ◽  
Pei-Xia Yang
Keyword(s):  
Projection Method ◽  
Minimization Problem ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Gradient Projection Method ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Gradient Projection Algorithm

We investigate the following regularized gradient projection algorithmxn+1=Pc(I−γn(∇f+αnI))xn,n≥0. Under some different control conditions, we prove that this gradient projection algorithm strongly converges to the minimum norm solution of the minimization problemminx∈Cf(x).

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